Question

Aroldis Chapman threw a fastball at 105.1 miles per hour on September 24, 2010, the record speed for a pitched baseball in a Major League Baseball game. If the ball was thrown at an angle exactly parallel to the ground, how far would the ball drop in the 16.8m between when it left Champan's hand and when it crossed home plate?

Answer 1

Answer on Question #46717-Physics-Other

Aroldis Chapman threw a fastball at $v_0 = 105.1$ miles per hour on September 24, 2010, the record speed for a pitched baseball in a Major League Baseball game. If the ball was thrown at an angle exactly parallel to the ground, how far would the ball drop in the $\Delta x = 16.8m$ between when it left Champan's hand and when it crossed home plate?

Solution

The horizontal displacement is

$$\Delta x = v_0 t.$$

The vertical displacement is

$$\Delta y = \frac{g t^2}{2}.$$

Therefore

$$\Delta y = \frac{g \left(\frac{\Delta x}{v_0}\right)^2}{2} = \frac{9.81 \frac{m}{s^2} \left(\frac{16.8m}{105.1 \cdot 0.44704 \frac{m}{s}}\right)^2}{2} = 0.627 \, m.$$

Answer: 0.627 m.

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