How tall is the building?

Question

A 0.43 kg rock is projected from the edge of the top of a building with an initial velocity of 11.1 m/s at an angle 50? above the horizontal. Due to gravity, the rock strikes the ground at a horizontal distance of 16.9 m from the base of the building. Assume the ground is level and that the side of the building is vertical. The acceleration of gravity is 9.8 m/s2. Answer in units of m.

Answer 1

Projectile problem. Let horiz range t +be R=16.9m.  Initial velocity is v=11.1 m/s.

X component of v is v_x = 11.1cos 50  = 7.13 m/s. Y component of v is v_y = 11.1 sin 50= 8.5 m/s

Let us calculate the time of flight t.  Since v_x is constant so velocity v_x = R/t.

t=16.9/7.13 = 2.37 sec

Consider the vertical part of the motion.

Δy = v_y t + 1/2 g t² = (8.5) 2.37 + 1/2 (9.8) (2.37)² = 20.15 -(4.9) (5.62) 

= -7.39 m