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 25 m/s
B) about 20 m/s
C) about 5 m/s
D) about 10 m/s
E) none of these

Question

Quizplus · Accepted Answer

The pitching speed can be determined by using the formula for horizontal distance traveled by a projectile: $d = v \times t$, where $d$ is the distance, $v$ is the horizontal velocity (pitching speed), and $t$ is the time of flight. The time of flight can be found from the vertical motion using the formula $y = \frac{1}{2} g t^2$, where $y$ is the vertical distance (5 m in this case) and $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$). Solving for $t$ gives $t = \sqrt{\frac{2y}{g}}$. Substituting $y = 5 m$ and $g = 9.8 m/s^2$ gives $t \approx \sqrt{\frac{2 \times 5}{9.8}} \approx \sqrt{\frac{10}{9.8}} \approx \sqrt{1.02} \approx 1.01$ seconds. Then, using $d = v \times t$ and $d = 20 m$, we find $v = \frac{d}{t} = \frac{20 m}{1.01 s} \approx 19.8 m/s$, which is about 20 m/s.

A Ball Player Wishes to Determine Pitching Speed by Throwing