Lab 4 Worksheet - Projectile Motion (Student).docx

Lab 4: Projectile Motion San Diego State University – Department of Physics Physics 195L – Fall 2022 Theory During projectile motion, there is only one force: the force due to gravity: . By integrating the above equation, we obtain the velocity vector as a function of time: where and are the x and y components of the initial velocity. Integrating again, we obtain the position vector: where and are the initial x and y coordinates of the projectile. In other words, , and . To simplify our equations, throughout this lab we will assume that , so , and . Range The first quantity we will be interested in calculating is the range of a projectile. This is equivalent to the maximum value of the x-component of , which is when is maximum. So how do we know when is maximum? After some thought, you should conclude that the maximum value of occurs when is equal to zero, i.e., when the projectile hits the ground. We can solve for by setting : We solve by factoring: , And so finally, is . To find the range we simply plug in into : . 1

PHYSICS 195L LAB REPORT - LAB 4: PROJECTILE MOTION Suppose that we know the initial speed and angle that the object will be launching from. (These are things we can measure.) We can write the components of the initial velocity vector as . Thus, the range can also be written as: Altitude calculation Instead of launching a projectile from and , imagine launching it from some nonzero altitude . To keep things simple, let's also assume that the object is launched with an initial vertical speed . Under these conditions, our general equation for : simplifies to: As you can see, the initial altitude h of the projectile depends only on and . Therefore, if we know the time of flight (the time when reaches 0) that a projectile is in motion, then we can solve for it’s initial altitude: Procedure Part I: Range 1. To make your results more consistent when launching the ball, always pull on the black cord (see Figure 1) with a quick short pulse. Do NOT pull slowly. Always make sure that everyone is clear before firing! 2. The angle should be set at 20°. Place the ball in the launcher and depress the plunger one "click" to the short range setting. 3. Launch the ball and note the landing location. Place a blank sheet of paper at this location and tape it in position as shown in Figure 2. Cover with a sheet of carbon paper. You do NOT need to tape the carbon paper. 2

PHYSICS 195L LAB REPORT - LAB 4: PROJECTILE MOTION Figure 3: Measuring the Range Figure 4: Launching from Center Figure 5: Landing Point Separation Figure 6: Horizontal Launcher Setup 4

PHYSICS 195L LAB REPORT - LAB 4: PROJECTILE MOTION Worksheet TA: Tony Ojeda Name: Lab partner: David Hu Date: Feb 22, 2023 Data Table 1: Range as a function of initial angle. Angle (degrees) Measured Range (m) Theoretical Range (m) Percent error (%) 20 0.83 =0.81m ((3. 53) 2 /9. 81)?𝑖?(2(20)) 0.83−0.81 0.81 | | | | 100 = 2. 47% 30 1.11 =1.10m ((3. 53) 2 /9. 81)?𝑖?(2(30)) 1.11−1.10 1.10 | | | | 100 = 0. 91% 40 1.23 =1.25m ((3. 53) 2 /9. 81)?𝑖?(2(40)) 1.23−1.25 1.25 | | | | 100 = 1. 60% 45 1.27 =1.27m ((3. 53) 2 /9. 81)?𝑖?(2(45)) 1.27−1.27 1.27 | | | | 100 = 0% 50 1.20 =1.25m ((3. 53) 2 /9. 81)?𝑖?(2(50)) 1.20−1.25 1.25 | | | | 100 = 4. 00% 60 1.05 =1.10m ((3. 53) 2 /9. 81)?𝑖?(2(60)) 1.05−1.10 1.10 | | | | 100 = 4. 55% 70 0.79 =0.81m ((3. 53) 2 /9. 81)?𝑖?(2(70)) 0.79−0.81 0.81 | | | | 100 = 2. 47% Table 2: Speed and time of flight Range setting Measured speed (m/s) Measured time of flight (s) Short (1) 3.55m/s 0.17s Short (1) 3.52m/s 0.18s Short (1) 3.54m/s 0.18s Medium (2) 4.62m/s 0.18s 5

PHYSICS 195L LAB REPORT - LAB 4: PROJECTILE MOTION Graph 1: Range as a function of initial angle (Insert Graph Here) 7