Answer to Question #244065 in Physics for Ding

Question

Projectile motion: other applications

A boy throws a rock with speed v = 18.3 m/s at an angel of theta = 57.0 over a building. The rock lands on the roof 15.0 m in the x direction from the boy. How long was the rock in the air? How much taller, height h, is the building than the boy? Ignore air resistance.

Answer 1

The time to pass the 25 m along the horizontal is

$$t=\frac{R}{v\cos\theta}=1.5\text{ s}.$$

The height of the point, thus, is

$$h=\frac{v_{yf}^2-v_{y0}^2}{2g}=\frac{(v\sin\theta-gt)^2-(v\sin\theta)^2}{2g}=12\text{ m}.$$