Projectile Motion Concept WS (Honors)

Projectile Motion concept WS answers

1. Which of the following moving objects would be considered to be projectiles?

o A punted football. Yes

o A falling skydiver with an open parachute. No, since vx = 0 and vertical acceleration is changing due to air resistance on parachute.

o A feather falling in a vacuum chamber. No, since vx = 0

o A small lead ball thrown horizontally from a height of 3 m. Yes

o An airplane flying through the sky. No, since the plane is continually propelled through the air.

2. Which of the following statements are true of projectiles?

o A projectile is a free-falling object. TRUE

o A projectile is always moving in the downward direction. FALSE (Only on the way down from the top.)

o A projectile must be accelerating in the downward direction. TRUE

o A projectile could begin its motion with a downward velocity. TRUE

3. Which of the following statements are true of the horizontal motion of projectiles?

o A projectile with a rightward component of motion will have a rightward component of acceleration. FALSE (A projectile has no horizontal acceleration.)

o The horizontal velocity of a projectile changes by 9.8 m/s each second. FALSE (The horizontal velocity is constant.)

o A projectile with a horizontal component of motion will have a constant horizontal velocity. TRUE

o The horizontal velocity of a projectile is 0 m/s at the peak of its trajectory. FALSE (It is a constant, non-zero value throughout its motion.)

o The horizontal velocity of a projectile is unaffected by the vertical velocity; these two components of motion are independent of each other. TRUE

o The horizontal displacement of a projectile is dependent upon the time of flight and the initial horizontal velocity. TRUE o The peak height reached by a projectile depends upon its horizontal velocity. FALSE (That depends only on the vertical part of its motion.)

o The final horizontal velocity of a projectile is always equal to the initial horizontal velocity. TRUE

o As a projectile rises towards the peak of its trajectory, the horizontal velocity will decrease; as it falls from the peak of its trajectory, its horizontal velocity will increase. FALSE (The horiz. velocity remains constant throughout.)

o Considering a projectile launched from ground level at a fixed launch speed and landing at ground level: the horizontal displacement (i.e., the range) of the projectile will increase as the angle of launch is increased from 0 degrees to 90 degrees. FALSE (It will increase until θ = 45° then it will continuously decrease.)

o Considering a projectile launched from ground level at a fixed launch angle and landing at ground level: the horizontal displacement (i.e., the range) of the projectile will always increase as the launch speed is increased. TRUE.

4. Which of the following statements are true of the vertical motion of projectiles?

o The vertical component of a projectile's velocity is constant. FALSE. (It decreases in magnitude going up and increases in magnitude coming down.)

o The vertical component of a projectile's velocity changes at a constant rate. TRUE (At a rate of 9.80 m/s every second.)

o A projectile with an upward component of motion will have an upward component of acceleration. FALSE (Acceleration is downward at every point.)

o A projectile will have a continuous downward acceleration throughout its motion. TRUE

o The magnitude of the vertical velocity of a projectile changes by 9.8 m/s each second. TRUE

o The vertical velocity of a projectile is 0 m/s at the peak of its trajectory. TRUE

o The vertical velocity of a projectile is unaffected by the horizontal velocity; these two components of motion are independent of each other. TRUE

o The final vertical velocity of a projectile is always equal to the initial vertical velocity. FALSE (Only if total vertical displacement – dy – is zero.) o The vertical acceleration of a projectile is 0 m/s² when it is at the peak of its trajectory. FALSE (The acceleration is 9.80 m/s² at every point in the path.) o As a projectile rises towards the peak of its trajectory, its acceleration is directed upward; as it falls from the peak of its trajectory, its acceleration is directed downward. FALSE (Acceleration is directed downward at every point in the path.)

o The peak height to which a projectile rises above the launch location is dependent upon the initial vertical velocity. TRUE

o As a projectile rises towards the peak of its trajectory, the vertical velocity will decrease; as it falls from the peak of its trajectory, its vertical velocity will increase. TRUE

o Consider a projectile launched from ground level at a fixed launch speed and landing at ground level: the peak height reached by the projectile will always increase as the angle of launch is increased from 0 degrees to 90 degrees. TRUE

o Consider a projectile launched from ground level at a fixed launch angle and landing at ground level: the peak height reached by the projectile will always increase as the launch speed is increased. TRUE

5. Two balls are rolling along a tabletop, ball A with twice the speed of ball B. Ball A starts from further back than B, however, so that the two balls roll off the edge of the table at the same instant. Which of the two balls reaches the floor first? Explain. They both hit the floor at the same instant. The horizontal speeds of the ball have no effect on their rates of fall. Both balls start from the same height and fall at the same rate.

6. Considering the aforementioned situation, how much further horizontally does A travel than B during its flight? Since ball A has twice the horizontal speed than B, it should travel TWICE the horizontal distance.

7. An expert marksman aims a high-powered rifle directly at a near target. Assuming that the rifle sight is adjusted accurately for distant targets, will the bullet hit the near target above or below the target center? Explain. It should hit ABOVE the target center. The “far-sighted” gun will have allowed for a greater vertical drop than what would have occurred during the short time of flight. The gun would have been angled upward too far.

8. In the diagram below, two different possible trajectories are shown for a ball thrown by a center fielder to home plate in a baseball game. Which of the two trajectories, A or B, will result in a longer time for the ball to reach home plate? Explain. A

B Since path A is higher, the ball would have spent a greater time in the air; therefore, it must have taken longer to get to home plate.

9. For the above diagram, assuming that the two trajectories represent throws by two different center fielders, which of the two is likely to be thrown by the player with the stronger arm? Explain. (Note: Launch angle, θ, for each is < 45°) Path B represents the throw by the stronger fielder. If the ball takes less time to travel, it must have had a greater velocity.

10. Back to the diagram again: how does the speed of the ball at the top of its path in A compare to the speed of the ball at the top of its path in B? At the top of the path, the ball’s vertical velocity is zero; only the horizontal component exists. Since ball B covered the same horizontal distance in less time, its horizontal velocity would have to be greater.

11. How does the speed of a projectile at the top of its trajectory compare to its original launching speed? (Assume θ > 0°) Give a mathematical relationship between those two speeds. The speed at the top would be less than its original speed since the vertical component is zero at the top (but is not zero at the launch).

vtop = vx = vo cosθ