The figure below shows the trajectory of a ball traveling through the air, affected by both gravity and air resistance.
Here are the positions of the ball at several successive times.
Location t (s) Position (m)
A 0.0 <0, 0, 0>
B 1.0 <22.8, 26.9, 0>
C 2.0 <39.4, 37.0, 0>
(a) What is the average velocity of the ball as it travels between location A and location B? (Express your answer in vector form.)
(b) If the ball continued to travel at the same average velocity during the next second, where would it be at the end of that second? (That is, where would it be at time t = 2 s? Express your answer in vector form.)
(c) How does your prediction from part (b) compare to the actual position of the ball at t = 2 s (location C)? If the predicted and observed locations of the ball are different, explain why.
rf is at the same point as what we predicted. We assumed constant velocity when making our prediction and an approximation of constant velocity is valid for any time interval.
rf is not at the same point as what we predicted. We assumed constant velocity when making our prediction; however, in reality the velocity was not constant, but was decreasing in both the x and y directions. An approximation of constant velocity is only valid for small time intervals. For this projectile, Δt = 1.0 s was not a small enough time interval to reasonably assume constant velocity.