Question

A baseball pitcher throws a fastball at a speed of 50.0 m/s. The acceleration occurs as the pitcher holds the ball in his hand and moves it through an almost straight-line distance of 4.2 m. Calculate the acceleration, assuming it is uniform. Compare this acceleration to the acceleration due to gravity, 9.8 m/s².

a. 12.5 m/s²
b. 4.2 m/s²
c. 9.8 m/s²
d. 50.0 m/s²

Answer 1

The acceleration of a baseball thrown by a pitcher that reaches a speed of 50.0 m/s over a distance of 4.2 m is 297.6 m/s², which is significantly larger than the acceleration due to gravity. The correct answer is not among the provided options.

Step-by-step explanation:

To calculate the acceleration of the baseball, we can use the kinematic equation which relates initial velocity, final velocity, acceleration, and distance traveled:

v2 = u2 + 2as, where:

• v is the final velocity (50.0 m/s).
• u is the initial velocity (0 m/s, as it starts from rest).
• a is the acceleration.
• s is the distance (4.2 m).

Plugging in the values and solving for a, we get:

(50.0 m/s)2 = (0 m/s)2 + 2 * a * 4.2 m

2500 m2/s2 = 2 * a * 4.2 m

a = 2500 m2/s2 / (2 * 4.2 m)

a = 297.6 m/s2

Comparing this to the acceleration due to gravity (9.8 m/s2), we can see that the ball's acceleration is significantly larger. The correct answer for the acceleration is not among the provided options.