Two-dimensional Motion Part 3

± Delivering a Package by Air A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land on, and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 442 at an altitude of 625 . The positive x and y directions are defined in the figure. For all parts, assume that the "island" refers to the point at a distance from the point at which the package is released, as shown in the figure. Ignore the height of this point above sea level. Assume that the free-fall acceleration is = 9.80 . Part A After a package is dropped from the plane, how long will it take for it to reach sea level from the time it is dropped? Assume that the package, like the plane, has an initial velocity of 442 in the horizontal direction. Express your answer numerically in seconds. Neglect air resistance. Hint 1. Knowns and unknowns: what are the initial conditions? Take the origin of the coordinate system to be at the point on the surface of the water directly below the point at which the package is released. The directions of the axes are shown in the figure in the problem introduction. In this coordinate system, what are the values of , , , of the package? Express your answers numerically and enter them, separated by commas, in the order , , , . Use units of meters and km/hour for distances and speeds, respectively. Hint 1. Initial velocity in the y direction Because the package is dropped horizontally, the vertical component of its initial velocity is zero. ANSWER: , , , = 0,625,442,0 Hint 2. What are the knowns and unknowns when the package hits the ground? Take the origin of the coordinate system to be at the point on the surface of the water directly below the point at which the package is released. The directions of the axes are shown in the figure in the problem introduction. Let be the time when the package hits the ground. In this coordinate system, 442 since there is no acceleration in the x direction. Which of the following values is/are known? Check all that apply. ANSWER: Hint 3. Find the best equation to use Which of the equations below could you use to find the time hits the ground? when the packet Hint 1. How to determine which equation to use Only one of the quantities , , is known. Which one? You have to use the equation that contains this variable. ANSWER: ANSWER: = 11.3 Correct Part B If the package is to land right on the island, at what horizontal distance to the island should the package be released? from the plane Express the distance numerically in meters. Hint 1. How to approach the problem You are asked to find , which is also the change in the x coordinate of the package over the time spent in the air. You should have calculated this time interval in Part A. Use it to find . Hint 2. The equation for Since there is no acceleration in the horizontal direction, the equation for is . ANSWER: = 1390 Correct Part C What is the speed of the package when it hits the ground? Express your answer numerically in meters per second. Hint 1. How to approach the problem The speed is the magnitude of the velocity, i.e., . You already know that 442 , so you need to find . Remember to be consistent in your usage of units when calculating your answer. Hint 2. The equation for the velocity in the y direction The equation for the velocity in the y direction is . If you have completed the earlier parts, you should know all the quantities on the right side. ANSWER: = 165 Correct Part D The speed at which the package hits the ground is really fast! If a package hits the ground at such a speed, it can be crushed and also cause some serious damage on the ground. Which of the following would help decrease the speed with which the package hits the ground? ANSWER: Increase the plane's speed and height Decrease the plane's speed and height Correct This is why it would be nice for rescue teams to have hybrid airplanehelicopters. Of course, then they can just airlift the stranded group. Problem 3.08 A projectile is fired from ground level at an angle of 62 speed of 28 . Part A above the horizontal with an initial What is the magnitude of its instantaneous velocity at the moment it is fired? Express your answer in meters per second to two significant figures. ANSWER: 28 Correct Part B What is the direction (relative to horizontal) of its instantaneous velocity at the moment it is fired? ANSWER: 0 with respect to the horizontal 62 above the horizontal 62 below the horizontal Correct Part C What is the magnitude of its instantaneous velocity the moment it reaches its maximum height? Express your answer in meters per second to two significant figures. ANSWER: 13 Correct Part D What is the direction (relative to horizontal) of its instantaneous velocity the moment it reaches its maximum height? ANSWER: 0 with respect to the horizontal 62 above the horizontal 62 below the horizontal Correct Part E What is the magnitude of its instantaneous velocity the moment before it hits the ground? Express your answer in meters per second to two significant figures. ANSWER: 28 Correct Part F What is the direction (relative to horizontal) of its instantaneous velocity the moment before it hits the ground? ANSWER: 0 with respect to the horizontal 62 above the horizontal 62 below the horizontal Correct Problem 3.12 A tennis ball rolls off the edge of a tabletop 0.650 above the floor and strikes the floor at a point 1.30 horizontally from the edge of the table. Part A Find the time of flight of the ball. ANSWER: = 0.364 Correct Part B Find the magnitude of the initial velocity of the ball. ANSWER: = 3.57 Correct Part C Find the magnitude of the velocity of the ball just before it strikes the floor. ANSWER: = 5.05 Correct Part D Find the direction of the velocity of the ball just before it strikes the floor. ANSWER: = 45.0 below the horizontal. Correct Problem 3.14 A daring 51 below. swimmer dives off a cliff with a running horizontal leap, as shown in the figure Part A What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom, which is = 2.40 wide and = 9.00 below the top of the cliff? Express your answer in meters per second to three significant figures. ANSWER: = 1.77 Correct