Question

A boy throws a rock with speed v = 18.3 m/s at an angle of θ = 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

(a) We can find the total flight time of the rock in the air from the kinematic equation:

$$x=v_{0x}t=v_0tcos\theta,$$ $$t=\dfrac{x}{v_0cos\theta}=\dfrac{15\ m}{18.3\ \dfrac{m}{s}\times cos57^{\circ}}=1.505\ s.$$

(b) We can find how much taller is the height of the building from another kinematic equation:

$$\Delta y=v_{0y}t+\dfrac{1}{2}gt^2,$$ $$\Delta y=v_0tsin\theta+\dfrac{1}{2}gt^2,$$ $$\Delta y=18.3\ \dfrac{m}{s}\times1.505\ s\times sin57^{\circ}+\dfrac{1}{2}\times(-9.8\ \dfrac{m}{s})\times(1.505\ s)^2,$$ $$\Delta y=12\ m.$$