Projectile Motion Lab Report

Objective: The kinematics of projectile motion in the earth’s gravitational field will be studied to gain an understanding of horizontal range, maximum height, time of flight, and trajectory of the projectile. Procedure: Table 1: 1) Connect each launcher photogate to the corresponding digital channel. Open the “Projectile1.ds” file. One shows the initial speed calculated from distance and time, and the other shows the projectile’s time of flight 2) Set the angle to 10, 20, 30, 45, 60, 70, and 80 degrees, push the projectile into the launcher and listen for three clicks. 3) Launch the projectile until it reaches the carbon paper and record the initial speed and time of flight from the given windows. Watch where it passes the vertical meter stick and record the maximum height. Table 2: 1) Set launcher to 70 degrees and position the whiteboard graph with the origin at the launch point. 2) Mark points on the whiteboard graph for every 5 centimeters, beginning at 5, and record the x and y coordinates. Analysis: To begin finding the data needed for Table 1, the initial velocity needed to be calculated. To do this calculation, the angle in the “Projectile1.ds” file was set to equal zero, and the projectile was pressed into the launcher on three separate occasions – hearing one click that rifled at 3.14 m/s, two clicks at 4.08 m/s, or three clicks at 5.26 m/s. It was then determined that the option with three clicks was the best option, as the projectile would be able to be launched with the greatest range. The time that was given from the “Projectile1.ds” file for each angle 𝟐∗𝐯𝒊 ∗𝐬𝐢𝐧(𝛉) ⁡ was very similar to the actual time value. To find the actual time value, the equation 𝐠 gets used, where vI is the initial velocity at 5.26 m/s, and g is the acceleration due to gravity, which is 9.8 m/s2. For example, at 10 degrees, the theoretical time found was 0.1817 seconds, and the actual time was 0.1864 seconds. Similarly, the theoretical range and maximum height 𝐠 for range and [𝐯𝒊 ∗𝐬𝐢𝐧(𝛉)]𝟐 ⁡ 𝐯𝒊 𝟐 ∗𝐬𝐢𝐧(𝟐𝛉) ⁡ were also very close to the actual values by using the equation 𝟐∗𝐠 for maximum height. Table 1 demonstrates that a projectile being launched at two different angles would travel the same horizontal distance, as long as both have the same initial velocity and have the summation of the two angles equal to 90 degrees. For instance, Table 1 shows a projectile getting launched at 20 degrees with an initial velocity of 5.26 m/s, which lands 1.815 meters away from the starting point. However, if the same object gets launched with the same velocity but at 70 degrees instead, the projectile would still land 1.815 meters away from the starting point. This is because the range of every projectile has two parameters – initial value of the horizontal velocity component and the time the projectile is in the air. A projectile that is launched at a higher angle would reach a greater height, which would cause for a longer hang time. However, with a greater time, the range will become limited because the horizontal velocity will be smaller. Likewise, a projectile launched at a smaller angle will have a smaller horizontal velocity, but the time would be short, which would also cause a limited range. The center of the 90 degrees (45 degrees) would have the greatest range because the horizontal velocity component would be the same as the vertical velocity component, meaning that the time of flight would be paired with the best horizontal velocity, making the projectile travel the furthest distance. Discussion: Overall, this experiment went very well and fairly accurate data was recorded. The percent errors ( |actual−theoretical| actual x 100%) for time, range, and maximum y were all less than 10%. It is nearly impossible to get perfect results, and human error plays a major factor into the errors. For example, the angles could not have been measured exactly, or the copper paper and launcher may not have been perfectly lined up. Another inaccuracy in this experiment relates to the copper paper. The paper is roughly a normal size of paper, so there is not just a single spot that the projectile could hit on the sheet. Instead, there is a wide range of different areas that are a possibility of being marked. These different locations can certainly have an effect on the total distance that it travels, which would also alter the time and possibly the maximum height as well. Changing even a single decimal place in this case may lead to a more accurate percent error. Conclusion: This lab was primarily focused on using kinematic equations for two dimensional motions. By using an initial velocity and an angle, the horizontal and vertical motions were able to get calculated, and showed that each location of a projectile can be predicted by simply using just a little bit of math.