Projectile Motion Review Questions Chapter 10

1. What exactly is a projectile? A projectile is anything that has a zero velocity that changes drastically when it accelerates. This could be many things, a football, a bullet, tennis ball. 2. Why does the vertical component of velocity for a projectile change with time, whereas the horizontal component of velocity doesn’t change? Vertical velocity for projectile objects components change when gravity allows there to be a vertical acceleration. A horizonal velocity however, continues constantly because there should not be any changes made. 3. A stone is thrown upward at an angle. What happens to the horizontal component of its velocity as it rises? As it falls? Because there is no horizontal force in the absence of air resistance, the horizontal velocity component remains constant. Whether the stone is rising or descending, this holds true. 4. A stone is thrown upward at an angle. What happens to the vertical component of its velocity as it rises? As it falls? The vertical velocity component of the stone reduces as it rises. The vertical velocity component increases as the stone falls. When the stone is hurled directly upward in 1-D motion, the vertical component is analyzed in the same way. 5. A projectile falls beneath the straight-line path it would follow if there were no gravity. How many meters does it fall below this line if it has been traveling for 1 s? For 2 s? In one second it sits at five meters and at two seconds twenty meters beneath the original location. 6. Do your answers to the preceding question depend on the angle at which the projectile is launched? No, the answers will remain the same regardless of the angle the objects are dropped at. 7. A projectile is launched upward at an angle of 70° from the horizontal and strikes the ground a certain distance downrange. For what other angle of launch at the same speed would this projectile land just as far away? The original angle is right around twenty degrees from where the projectile lands. 8. A projectile is launched vertically at 100 m/s. If air resistance can be ignored, at what speed will it return to its initial level? When you ignore air resistance then nothing changes and the speed will both “return” and continue at its initial speed of one hundred meters per second. 9. How can a projectile “fall around the Earth”? If a projectile at a given height has the necessary tangential speed v, it can "fall around the Earth." It will have moved a horizontal distance vt and fallen a vertical distance 12gt2 below the horizontal after an elapsed period t. The projectile will be at the same height above the surface if the Earth's surface slopes downward by exactly that distance. 10. How does Earth’s curvature relate to the speed needed for a projectile to orbit Earth? The curvature and the speed v are inextricably linked. It will have moved a horizontal distance vt and fallen a vertical distance 12gt2 below the horizontal after an elapsed period t. The projectile will be at the same height above the surface if the Earth's surface slopes downward by exactly that distance. 11. Why is it important that the projectile in the preceding question be above Earth’s atmosphere? If the object were to travel through the atmosphere, air resistance would soon slow it down, and difference in temperature would immediately burn it up. 12. Why doesn’t the force of gravity change the speed of a bowling ball as it rolls along a bowling lane? There is no centrifugal force that acts in the path of motion of the ball. Gravity conducts no work on the ball, therefore its kinetic energy or speed remain unchanged. 13. Why doesn’t the force of gravity change the speed of a satellite in circular orbit? There is no gravitational pull acting in the direction of the satellite's travel. The satellite's velocity is always tangential to its rotation in a highly elliptical orbit, and the gravitational attraction on it is always directed radially. Gravity has no effect on the satellite and so has no effect on its kinetic energy or speed. The beauty of the sunset was obscured by the industrial cranes 14. How much time does it take for a complete revolution of a satellite in close orbit about the Earth? The revolution will be completed in around ninety minuets or an hour and a half. 15. For orbits of greater altitude, is the period longer or shorter? The time it takes the satellite that far away from earth is most definitely longer than the 90 minuets it previously took. Near-Earth satellites have a period of around 90 minutes. Their orbital speed slows as they rise in altitude, while their period lengthens. The beauty of the sunset was obscured by the 16. Why does the force of gravity change the speed of a satellite in an elliptical orbit? There is usually always a component of gravitational force in the direction of motion when a satellite is in an elliptical orbit, exerting work and modifying the satellite's KE. It slows down as it gets farther away from the Earth, then picks up speed as it gets closer. The beauty of the sunset was obscured by the 17. At what part of an elliptical orbit does an Earth satellite have the greatest speed? The lowest speed? When the satellite is closest to the Earth, it moves the fastest, and when it is farthest from the Earth, it moves the slowest. As the satellite gets farther away from the Earth, it slows down, and as it gets closer, it picks up speed again. The beauty of the sunset was obscured by the industrial cranes 18. Who gathered the data that showed planets traveling in elliptical paths around the Sun? Who discovered elliptical orbits? Who explained them? The beauty of the sunset was obscured by the Brahe, Tycho Johannes Kepler was a German mathematician. Newton, Isaac. industrial cranes 19. What did Kepler discover about the periods of planets and their distances from the Sun? The period squared is directly proportional to the average radial distance cubed, according to Kepler's third law. The beauty of the sunset was obscured by the industrial cranes 20. What was the direction of the force on a planet in Kepler’s thinking? In Newton’s thinking Kepler, like Aristotle, believed that a moving planet's force would be in the direction of motion. Newton discovered that things in orbit are drawn toward the body around which they orbit, therefore the force on a moving planet is directed toward the Sun. The beauty of the sunset was obscured by the industrial 21. Why is kinetic energy a constant for a satellite in a circular orbit but not for a satellite in an elliptical orbit? The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset was Because of the conservation of energy, the total of KE and PE remains constant. When a satellite is in a circular orbit, its distance from the attracting body's center is constant, hence its PE remains constant. As a result, its KE remains constant. The distance changes when a satellite is in an elliptical orbit. The satellite slows down as PE increases and KE reduces as it goes farther away from the Earth, and it speeds up as PE falls and KE grows as it gets closer to the Earth. The whole energy is conserved, i.e. it remains constant. The beauty of the sunset was obscured by the industrial cranes 22. Is the sum of kinetic and potential energies a constant for satellites in circular orbits, in elliptical orbits, or in both? The beauty of the sunset was obscured by the industrial cranes Both. The sum of KE and PE for an object in orbit, whether circular or elliptical, is constant. 23. Escape speed from Earth is 11.2 km/s. Is it possible to escape from Earth at half this speed? At onequarter this speed? If so, how? Projectile Any object that moves through the air or through space under the influence of gravity. Parabola The curved path followed by a projectile under the influence of only constant gravity. Satellite A projectile or small celestial body that orbits a larger celestial body. Ellipse The oval shaped path followed by a satellite. The sum of the distances from any point on the path to two points called foci is a constant. When the foci are together at one point, the ellipse is a circle. Yes and yes and yes The beauty of the sunset was obscured by the industrial cranes The beauty of the 24. With a stick and strings, make a “trajectory stick” as shown on page 187. The beauty of the sunset You may demonstrate the theory in Figures 10.7 and 10.8 by holding the stick at various angles away from the horizontal. A projectile's vertical distance below the idealized straight route depicted by the meter stick is the distance it would fall if it were released from rest. This is independent of the angle of launch. The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset was 26. A ball is thrown horizontally from a cliff at a speed of 10 m/s. You predict that its speed 1 s later will be slightly greater than 14 m/s. Your friend says it will be 10 m/s. Show who is correct. This is very correct yep this do be right The beauty of the sunset was obscured by the industrial cranes 28. Bull’s-eye Bob at a hunting range fires his rifle at a target 200 meters downrange. The bullet moves horizontally from the rifle barrel with a speed of 400 m/s. (a) How far does the bullet drop from a straight-line horizontal path by the time it reaches the target? (b) To hit a bull’s-eye why does Bob adjust his gunsight so the barrel points a bit upward when he aims at the target? The beauty of the sunset was The bullet travels at 0.5 seconds and as far as 1.25 meters. The beauty of the sunset was obscured by t 30. Students in the lab (see Figure 10.5) measure the speed of a steel ball to be 8.0 m/s when launched horizontally from a 1.0-m-high tabletop. Their objective is to place a 20-cm-tall coffee can on the floor to catch the ball. Show that they score a bull’s-eye when the can is placed 3.2 m from the base of the table. The time is 0.4 seconds and then 3.2 meters. The beauty of the sunset was obscured by the industrial 32. A certain satellite has a kinetic energy of 8 billion joules at perigee (the point closest to Earth) and 5 billion joules at apogee (the point farthest from Earth). As the satellite travels from apogee to perigee, how much work does the gravitational force do on it? Does its potential energy increase or decrease during this time, and by how much? The beauty of the sunset was obscured by the industrial cranes 3,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000 Yes, the PE falls by three billion J. 34. A horizontally moving tennis ball barely clears the net, a distance y above the surface of the court. To land within the tennis court, the ball must not be moving too fast. (a) To remain within the court’s border, a horizontal distance d from the bottom of the net, show that the ball’s maximum speed over the net is v = d B 2y g (b) Suppose the height of the net is 1.00 m, and the court’s border is 12.0 m from the bottom of the net. Use g = 10 m/s2 and show that the maximum speed of the horizontally moving ball clearing the net is about 27 m/s (about 60 mi/h). (c) Does the mass of the ball make a difference? Defend your answer. The beauty of the sunset was obscured by the industrial cranes a. In terms of vertical motion, the tennis ball begins at rest and drops y meters. Relate the height loss to the passage of time. b. To get v = 26.8 m/s, plug the numbers into the equation you just derived. No. The ball is falling freely, and its acceleration is unaffected by its mass. The beauty of the sunset was obscured 36. A ball is tossed off the edge of a cliff with the same speed but at different angles, as shown. From greatest to least, rank the A B C (a) initial PEs of the balls relative to the ground below. (b) initial KEs of the balls when tossed. (c) KEs of the balls when they hit the ground below. (d) times of flight while airborne. The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset was a. A=B=C. b. A=B=C. c. A=B=C d. B, A, C. The beauty of the sunset was obscured by the industrial cranes 38. The positions of a satellite in elliptical orbit are indicated. Rank these quantities from greatest to least: A B C D (a) Gravitational force (e) PE (b) Speed (f) Total energy (KE + PE) (c) Momentum (g) Acceleration (d) KE. The beauty of the sunset was obscured by the industrial cranes The beauty of the a. A, B, C, D. b. A, B, C, D. c. A, B, C, D. d. A, B, C, D. e. D, C, B, A. f. A=B=C=D. g. A, B, C, D. 40. Suppose you roll a ball off a tabletop. Will the time to hit the floor depend on the speed of the ball? (Will a fast ball take a longer time to hit the floor?) Defend your answer. No. The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset was 42. If you toss a ball vertically upward in a uniformly moving train, it returns to its starting place. Will it do the same if the train is accelerating? Explain. No. The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset was 44. Suppose you drop a care package from an airplane traveling at constant velocity, and further suppose that air resistance doesn’t affect the falling package. What will be its falling path as observed by someone at rest on the ground, not directly below but off to the side where there’s a clear view? What will be the falling path as observed by you looking downward from the airplane. Where will the package strike the ground, relative to you in the airplane? Where will it strike in the more realistic case in which air resistance does affect the fall? The beauty of the sunset was obscured by the industrial cranes The As seen from the ground, the path of the falling object will be a parabola . The object falls straight down along a vertical path in your reference frame on the plane, with no air resistance. From your vantage point, it lands exactly beneath you. When we consider the impacts of air resistance on the care package in a more realistic scenario, air resistance diminishes the forward-directed horizontal component of velocity. We anticipate it landing behind the airliner. The beauty of the sunset was obscured by the 46. In the absence of air resistance, why doesn’t the horizontal component of a projectile’s motion change, while the vertical component does? The beauty of the sunset was obscured by the industrial Because there is no horizontal force, the horizontal velocity component remains constant (in the absence of air resistance). Because gravity generates a vertical acceleration, the vertical velocity component changes. The beauty of the sunset was obscured by the industrial cranes 48. When a rifle is being fired at a distant target, why isn’t the barrel aligned so that it points exactly at the target? The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset was Because the top is in the same position as it always has been and will not change. obscured by the 50. A park ranger shoots a monkey hanging from a branch of a tree with a tranquilizing dart. The ranger aims directly at the monkey, not realizing that the dart will follow a parabolic path and thus will fall below the monkey. The monkey, however, sees the dart leave the gun and lets go of the branch to avoid being hit. Will the monkey be hit anyway? 204 part One Mechanics Does the velocity of the dart affect your answer, assuming that it is great enough to travel the horizontal distance to the tree before hitÝng the ground? Defend your answer. The beauty of the sunset was obscured by the industrial cranes Both are 1 meter per second starting from the acceleration then dividing the force five mass and multiplying by either 1 Newton or two newtons but you still end up with the exact same answer so it doesn't really matter. The beauty of the sunset was obscured by the industrial cranes 52. When you jump upward, your hang time is the time your feet are off the ground. Does hang time depend on your vertical component of velocity when you jump, your horizontal component of velocity, or both? Defend your answer. The beauty of the sunset was obscured by the industrial cranes Negative 45 meters per second squared and 4500 newtons after calculating the magnitude of the net horizontal force The beauty of the sunset was obscured by the industrial cranes The beauty of the 54. Since the Moon is gravitationally attracted to Earth, why doesn’t it simply crash into Earth? D, A=B=C and then A=C, B=D The beauty of the sunset was obscured by the industrial cranes 56. When a satellite coasts in a circular orbit at constant speed about Earth, is it accelerating? If so, in what direction? If not, why not? a. A=B=C b. C, A, B The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset was obscured by the industrial cranes 58. Upon which does the speed of a circling satellite not depend: the mass of the satellite, the mass of Earth, the distance of the satellite from Earth? The beauty of the sunset was obscured by the industrial When you lose contact with the ball, the force you apply on it stops. The beauty of the sunset was 60. If you have ever watched the launching of an Earth satellite, you may have noticed that the rocket starts vertically upward, then departs from a vertical course and continues its climb at an angle. Why does it start vertically? Why doesn’t it continue vertically? Yes and also not The beauty of the sunset was obscured by the industrial cranes The beauty of the \ 62. When a satellite in circular orbit slows, perhaps due to the firing of a “retro rocket,” it ends up gaining more Because of its lesser gravity, objects weigh less on the moon. Each apple weighs less on the moon than it does on Earth. On the moon, a 1-pound bag of apples contains more apples. On Earth, a one-kilogram bag of apples holds the same quantity of apples as it does on the moon or anywhere else. The mass remains the same. speed than it had initially. Why? The beauty of the sunset was obscured by Because of its lesser gravity, objects weigh less on the moon. Each apple weighs less on the moon than it does on Earth. On the moon, a 1-pound bag of apples contains more apples. On Earth, a one-kilogram bag of apples holds the same quantity of apples as it does on the moon or anywhere else. The mass remains the same. The beauty of the sunset was obscured by the industrial cranes The beauty of the 64. Ignoring air resistance, could a satellite be put into orbit in a circular tunnel beneath Earth’s surface? Discuss. The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset was Allow the boxes to float in front of you before gently nudging them. The box with the most mass and sand is the one that provides the greatest resistance to acceleration. The beauty of the sunset was 66. Why is work done by the force of gravity on a satellite when it moves from one part of an elliptical orbit to another, but no work is involved when it moves from one part of a circular orbit to another? Literately nope. The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset 68. If a satellite circled Earth at a distance equal to the Earth– Moon distance, how long would it take for it to make a complete orbit? In other words, what would be its period? The beauty of the sunset was The amount of stuff/matter in something is measured by mass, which does not change when the junk car is crushed. Its weight does not change because it remains on Earth. The beauty of the sunset was 70. What happens to an Earth satellite’s period when the satellite is placed into a higher orbit? The scale reading will grow as you throw the object while keeping your hand in contact with it. 72. How could an astronaut in a space shuttle “drop” an object vertically to Earth? At the Earth's surface, one kilogram of mass weighs 2.2 pounds. If you weigh 154 pounds, for example, your mass equals (154lb)/(2.2lb/kg)=70kg. Using weight=mg, your weight in newtons is (70kg)(10N/kg)=700N. The beauty of the sunset was obscured by the industrial cranes 74. A satellite in a circular orbit about the Moon fires a small probe in a direction opposite to the velocity of the satellite. If the speed of the probe relative to the satellite is the same as the satellite’s speed relative to the Moon, describe the motion of the probe. If the probe’s relative speed is twice the speed of the satellite, why would it pose a danger to the satellite? The beauty of the sunset was Because the crate is at rest, the net force acting on it is zero. The floor's friction force on the crate is equal to and opposed to the force you're exerting, F. The beauty of the sunset was obscured by the 76. If you stopped an Earth satellite dead in its tracks, it would simply crash into Earth. Why, then, don’t the communications satellites that “hover motionless” above the same spot on Earth crash into Earth ? To the front of the vehicle. The beauty of the sunset was obscured by the industrial cranes 78. Which requires less fuel: launching a rocket to escape speed from the Moon or from Earth? Defend your answer. The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset According to Newton's second law, acceleration is defined as the ratio of net force to mass. Because the net force on an item in free fall is weight, the acceleration is weight/mass = mg/m = g, which is the same for all masses. In other words, the more massive object's larger gravitational force is exactly matched by that mass's greater inertia, therefore all objects in free fall accelerate at the same rate, g. 80. As part of their training before going into orbit, astronauts experience weightlessness when riding in an airplane that is flown along the same parabolic trajectory as a freely falling projectile. A classmate says that gravitational forces on everything inside the plane during this maneuver cancel to zero. Another classmate looks to you for confirmation. What is your response? Zero newtons The beauty of the sunset was obscured by the industrial cranes he beauty of the sunset 82. At what point in its elliptical orbit about the Sun is the acceleration of Earth toward the Sun a maximum? At what point is it a minimum? Defend your answers. The beauty of the sunset was obscured The velocity of the tossing coin diminishes as it ascends. If we ignore air resistance, the acceleration stays the same. The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset 84. A friend claims that bullets fired by some high-powered rifles travel for many meters in a straightline path before they start to fall. Another friend disputes this claim and states that all bullets from any rifle drop beneath a straight-line path a vertical distance given by 1 2 gt 2 and that the curved path is apparent for low velocities and less apparent for high velocities. Now it’s your turn: Discuss whether or not all fired bullets drop the same vertical distance in equal times. Ten meters per seconds squared directed to the ground The beauty of the sunset was obscured by the 86. Would the speed of a satellite in close circular orbit about Jupiter be greater than, equal to, or less than 8 km/s The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset On Earth, a Newton's cannon must travel at a speed of 8 km/s. Jupiter's gravitational pull is stronger than Earth's, increasing the required speed because the projectile would fall a longer distance in the same amount of time. Furthermore, because Jupiter is so much bigger than Earth, the ground is much closer to being flat, therefore the cannonball would have to be launched considerably faster to "fall around Jupiter." Table 10.1 further validates the answer because a quantitative study indicates that the needed speed of Newton's cannon is the planet's escape speed divided by two. The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset was obscured by the industrial cranes 88. Discuss why Hawaii is the most efÏcient launching site in the United States for nonpolar satellites. In your discussion include a look at the spinning Earth from above either pole and compare it to a rotating turntable. The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset was Hawaii is closer to the equator than the rest of the United States. The equator's points are the furthest from the spin axis, hence they have the fastest tangential speed (see page 134). The most powerful boost to a rocket comes from launching near the equator. The Earth seems to be rotating counterclockwise when viewed from above the north pole, and Hawaii is closer to the rim than any other location in the United States. The beauty of the sunset was obscured by the industrial cranes 90. A communications satellite with a 24-hour period hovers over a fixed point on Earth and, to Earth observers, seems motionless. Why is it placed only in an orbit in the plane of Earth’s equator? In your discussion, think of the satellite’s orbit as a ring around Earth. The beauty of the sunset was obscured Geosynchronous communication satellites have a 24-hour period, similar to the Earth's rotation, and hence appear to hang above a fixed point, P, on the planet. As a result, the satellite travels on a circular route, the center of which is the Earth's core. This satellite must also follow a circular course with the Earth's center in order to remain exactly overhead at point P. Only if point P is on the equator is this true. The beauty of the sunset was obscured by the industrial cranes The beauty of the sunset wacranes 92. In 2000–2001, NASA’s Near Earth Asteroid Rendezvous (NEAR) spacecraft orbited around the 20mile-long asteroid Eros. Do you speculate that the orbital speed of this spacecraft is greater or less than 8 km/s? Discuss and defend your answer. Te beauty of the sunset was obscured by the industrial cranes The speed is less than 8 km/s. The beauty of the sunset was obscured by the industrial cranes 94. Why does a satellite burn up when it descends into the atmosphere? And why doesn’t it burn up when it ascends through the atmosphere? The beauty of the sunset was obscured by the industrial cra A descending satellite travels through the atmosphere at the tangential speed required to keep its orbit, which is extremely rapid. It is largely travelling vertically upward as it ascends through the atmosphere. It's important to note that it's not traveling as quickly as an orbital body would at that altitude. The rising satellite does not achieve orbital velocity until it has passed through the majority of the atmosphere. The beauty of the sunset was obscured by the industrial cranes The beauty of the sunse 96. You read in an article about astronauts in a major magazine that “about 62 miles up, the atmosphere ends and gravity becomes very weak. . . .” What error is made here? The beauty of the sunset was The mistake was to believe that because the astronauts don't feel weighted, gravity isn't exerting much force on them. Gravity at a height of 62 miles is almost as powerful as it is on Earth's surface, according to calculations, yet the astronauts are in free fall and thus feel weightless. It's also a misconception that the atmosphere quits suddenly around 62 miles altitude. 98. In an accidental explosion, a satellite breaks in half while in circular orbit about Earth. One half is brought momentarily to rest. What is the fate of the half brought to rest? Discuss what happens to the other half. The beauty of the sunset was obscured by the industrial cranes Half of the satellite will fall vertically straight down to Earth if it comes to a halt. We conclude that the second half will achieve twice the satellite's original velocity based on linear momentum conservation. It will move away from Earth. Mv=(M2)(0)+(M2)(2v) According to a more rigorous computation, the orbital speed will be twice that of Earth's escape speed, allowing the second piece to escape Earth's gravity and sail into the wild blue yonder. 100. A rocket coasts in an elliptical orbit around Earth. To attain the greatest amount of KE for escape for a given amount of fuel, should it fire its engines to accelerate forward when it is at the apogee or at the perigee? (Hint: Let the formula Fd 5 DKE be your guide to thinking. Suppose the thrust F is brief and of the same duration in either case. Then consider the distance d the rocket would travel during this brief burst at the apogee and at the perigee.) Make use of the Fd=KE link between work and energy. The maximum work done happens when d is highest for a constant thrust F of fixed duration. This will result in the greatest change in KE. The rocket will travel the greatest distance at the time interval when it is moving the quickest, which is at the perigee.