Answer to Question #124628 in Physics for jn

Question

A baseball is hit at a velocity of 100fps at an angle 20° above the horizontal. Will the ball hit a fence 20ft high and 200ft away from the batter’s plate? How far will the ball land from the fence?

Answer 1

$$v\cos{20}t=x\to 100\cos{20}t=200\\t=2.13\ s$$

$$y=v\sin{20}t-0.5gt^2\\=100\sin{20}(2.13)-0.5(32.17)(2.13)^2\\=-0.13\ ft<20\ ft$$

The ball doesn't hit a fence.

$$d=x-R=x-\frac{v^2}{g}\sin{40}\\=200-\frac{100^2}{32.17}\sin{40}=0.19\ ft$$