Answer to Question #102289 in Mechanics | Relativity for Sarah Gustafson

Question

A home run is hit in such a way that the baseball just clears a wall 20.0 m high, located 136 m from home plate. The ball is hit at an angle of 37.0° to the horizontal, and air resistance is negligible. (Assume that the ball is hit at a height of 1.0 m above the ground.)

Answer 1

We need to find the initial speed of the ball.

The time to reach the fence is

$$t=\frac{x}{v\cos{37}}=\frac{136}{v\cos{37}}$$

$$y=y_0+v\sin{37}t-0.5gt^2$$

$$20=1+v\sin{37}\left(\frac{136}{v\cos{37}}\right)-0.5(9.8)\left(\frac{136}{v\cos{37}}\right)^2$$

$$v=41.3\frac{m}{s}$$