Question

1. -/1 points a baseball pitcher throws a ball at 90.0 mi/h in the horizontal direction. how far does the ball fall vertically by the time it reaches home plate, which is a horizontal distance of 60.5 ft away? (express your answer in units of feet. neglect air resistance.) ft resources

Explanation:

Step1: Convert speed to ft/s

First, convert 90.0 mi/h to ft/s. 1 mile = 5280 ft and 1 hour = 3600 s. So, $v = 90\times\frac{5280}{3600}=132$ ft/s.

Step2: Find time of flight

Use the horizontal - motion formula $x = v_x t$. Since $v_x=v = 132$ ft/s and $x = 60.5$ ft, then $t=\frac{x}{v_x}=\frac{60.5}{132}$ s.

Step3: Find vertical displacement

Use the vertical - motion formula for free - fall $y=\frac{1}{2}gt^2$, where $g = 32.2$ ft/s². Substitute $t=\frac{60.5}{132}$ s into the formula: $y=\frac{1}{2}\times32.2\times(\frac{60.5}{132})^2$.
$y=\frac{1}{2}\times32.2\times\frac{60.5^2}{132^2}=\frac{16.1\times3660.25}{17424}\approx3.39$ ft.

Answer:

3.39