A ball player wishes to determine pitching speed by throwing a ball horizontally from an elevation of 5 m above the ground.The player sees the ball land 20 m down range.What is the player's pitching speed?
A)about 5 m/s
B)about 10 m/s
C)about 20 m/s
D)about 25 m/s
E)none of these

Question

Quizplus · Accepted Answer

First, we must convert the given measurements into SI units. 5 m elevation becomes the initial vertical displacement (y0) of the ball and 20 m distance becomes the horizontal displacement (x). The acceleration of the ball is due to gravity, which is approximately 9.81 m/s^2.

We can use the kinematic equation for horizontal motion:

x = v0xt

where v0x is the initial horizontal velocity and t is the time it takes for the ball to travel 20 m assuming a constant acceleration of 0 m/s^2 in the horizontal direction. Solving for time:

t = x / v0x

For the vertical motion, we can use the kinematic equation:

y = y0 + v0y t + 1/2 a t^2

where v0y is the initial vertical velocity (0 since the ball is thrown horizontally) and y is the final vertical displacement, which is also 0 as the ball lands on the ground. Solving for v0x:

v0x = x / t

Using the time expression derived earlier:

v0x = x / (x / v0x)

v0x^2 = x * g

v0x = sqrt(x * g)

Plugging in the given values:

v0x = sqrt(20 m * 9.81 m/s^2) ≈ 19.8 m/s

Rounding to the nearest 10, the answer is approximately 20 m/s, which is choice C.

A Ball Player Wishes to Determine Pitching Speed by Throwing