Question

a pitcher throws a softball toward home plate. when the ball hits the catchers mitt, its horizontal velocity is 32 meters/second. the softballs velocity goes to 0 meters/second in 0.8 seconds when caught. if the softball has a mass of 0.2 kilograms, whats the force of the impact? use f = ma, where a = \\(\frac{v - u}{t}\\). the force of the impact is newtons.

Explanation:

Step1: Calculate the acceleration

The initial horizontal velocity $u = 32$ m/s, the final velocity $v=0$ m/s, and the time $t = 0.6$ s. Using the formula $a=\frac{v - u}{t}$, we substitute the values: $a=\frac{0 - 32}{0.6}=\frac{- 32}{0.6}=-\frac{160}{3}$ m/s².

Step2: Calculate the force

We know that $F = ma$, where $m = 0.2$ kg and $a=-\frac{160}{3}$ m/s². Substituting the values, we get $F=0.2\times(-\frac{160}{3})=-\frac{32}{3}\approx - 10.67$ N. The magnitude of the force is $\frac{32}{3}\approx10.67$ N.

Answer:

$10.67$