PHYS 253 - Module 2 - Lab 5

2-D Kinematics and Projectile Motion PRE-LAB QUESTIONS 1. In one of your experiments, you will roll a marble down a ramp to provide an initial horizontal velocity. Suppose you start the marble at rest (vo = 0 m/s) and it travels a distance of, d, down the ramp. Use 1-D kinematics to predict the velocity of the ball (vf ) at the bottom of the ramp. Hint: the acceleration of the ball down the ramp is 9.81*sin(θ) m/s2 where θ is the angle of the ramp. Record you answer in variables (you will calculate the velocity with magnitudes when you perform the experiment). 2. Use the kinematic equations to derive a general equation for the time it takes a ball dropped from rest at vertical height, h, to reach the ground. 3. Use the result from Question 2 to write a general equation for the distance travelled by a projectile that is rolling off a table of height, h, with a horizontal speed, v0x. 4. The range of projectiles is dependent on the velocity and angle of the launch. Use the kinematic equations to prove the range of a projectile launched at velocity, v, and angle, θ, is equal to R = v 2 g sin ( 2 θ ) . Hint : The velocity at the beginning and end of the motion has the same magnitude, but opposite direction. 5. Prove that launching a projectile at 45° provides the largest range. a. Write the range as a function of Θ. b. Take the derivative of the range with respect to Θ and find the maximum angle. ©eScience Labs, 2014

2-D Kinematics and Projectile Motion EXPERIMENT 1: DISTANCE TRAVELED BY A PROJECTILE Data Sheet Table 1. Range and Velocity of Projectile at Ramp Distance 1 Ramp Incline (degrees) 50 ° Ramp Distance (m): 0.035 m Trial Measured Distance (m) 1  0.045 m 2  0.04 m 3  0.044 m 4  0.05 m Average  0.04475 m Table 2. Range and Velocity of Projectile at Ramp Distance 2 Ramp Distance (m):   0.03 m Trial Measured Distance (m) 1  0.06 m 2  0.055 m 3  0.065 m 4  0.06 m Average  0.06 m Table 3. Range and Velocity of Projectile at Ramp Distance 3 ©eScience Labs, 2014

2-D Kinematics and Projectile Motion 3. If you were to fire a paintball pellet horizontally, at a set height, and at the same time drop an identical pellet from the same set height you fired from the paintball gun, predict which pellet would hit the ground first. Explain your reasoning. The two paintball pellets would hit the ground at the same time. The pellet’s horizontal and vertical components of motion are independent from one another. The pellet traveling forward is experiencing similar downward vertical acceleration due to gravity as the pellet being dropped straight down. 4. Suppose you altered your existing ramp so that the marbles had twice their initial velocity right before leaving the ramp. How would this change the total distance traveled by the marbles? Cite the kinematic equations (or variations of them) to support your answer. R = v 2 sin ( 2 θ ) g From the given range equation, we find that the total distance of the marble would increase by four times, given an increase in initial velocity of two times. 5. Describe the acceleration of the marble after it leaves the ramp. The marble only has a downward vertical acceleration due to gravity (neglecting air resistance). This downward acceleration is what causes the parabolic travel path that is projectile motion. ©eScience Labs, 2014

2-D Kinematics and Projectile Motion EXPERIMENT 2: SQUEEZE ROCKET TM PROJECTILES Data Sheet Table 5. Projectile Data for Rockets with Different Launch Angles Launch Velocity (m/s) Initial Angle Time (s) Average Time (s) Predicted Range (m) Actual Range (m) Average Range (m) Range % Error   90 °               90 °           90 °           90 °           Student Selects:               Student Selects:           Student Selects:           Student Selects:           Student Selects:               Student Selects:           Student Selects:           Student         ©eScience Labs, 2014