Ryan throws a tennis ball vertically upward. The ball returns to the point of release after 3.5 s. What is the speed of the ball as it is released?
A)0 m/s
B)14 m/s
C)17 m/s
D)21 m/s
E)34 m/s

Question

Quizplus · Accepted Answer

We can use the kinematic equation:

h = vi*t + (1/2)*a*t^2

Where:
h = maximum height reached (equal to initial height)
vi = initial velocity (what we're looking for)
t = time of flight (3.5 s)
a = acceleration due to gravity (-9.81 m/s^2)

Setting h = 0 (since the ball returns to the point of release), we get:

0 = vi*(3.5 s) + (1/2)*(-9.81 m/s^2)*(3.5 s)^2

Solving for vi, we get:

vi = (1/2)*(-9.81 m/s^2)*(3.5 s) = -17.12 m/s

The negative sign indicates that the velocity is directed downward (i.e. opposite to the positive direction of motion).

However, the question asks for the speed of the ball (i.e. its magnitude, regardless of direction), so we take the absolute value:

|vi| = 17.12 m/s ≈ 17 m/s

Therefore, the best choice is C.

Ryan Throws a Tennis Ball Vertically Upward