Question

A fastball pitcher can throw a baseball at a speed of 40 m/s (90 mi/h). (a) Assuming the pitcher can release the ball 16.7 m from home plate so the ball is moving horizontally, how long does it take the ball to reach home plate? (b) How far does the ball drop between the pitcher’s hand and home plate?

a) 0.42 s, 3.7 m
b) 0.84 s, 7.4 m
c) 0.42 s, 7.4 m
d) 0.84 s, 3.7 m

Answer 1

The time it takes for a fastball to reach home plate is 0.42 seconds, and the ball drops 3.7 meters due to gravity during that time. The correct answer is option a).

Step-by-step explanation:

Solving the Baseball Pitch Problem

To answer part (a) of the question regarding the time it takes for a fastball to reach home plate, we can use the formula for constant speed: time = distance / speed. Given the distance is 16.7 m and the speed is 40 m/s, the time it takes for the ball to reach home plate is 16.7 m / 40 m/s = 0.4175 seconds, which can be rounded to 0.42 seconds.

For part (b), we need to calculate how far the ball drops due to gravity in that time. We use the formula for free fall distance, which is d = 0.5 * g * t^2 where g is the gravitational acceleration (9.8 m/s²) and t is the time. Plugging in the numbers, we get d = 0.5 * 9.8 m/s² * (0.42 s)^2 = 3.67 m, which can be rounded to 3.7 m.

The correct answer therefore is (a) 0.42 s and (b) 3.7 m, which corresponds to option a).