Question

A 0.56 kg rock is projected from the edge of the top of a building with an initial velocity of 7.57 m/s at an angle 53◦ above the horizontal. Due to gravity, the rock strikes the ground at a horizontal distance of 10.5 m from the base of the building.

How tall is the building? Assume the ground is level and that the side of the building is vertical. The acceleration of gravity is 9.8 m/s^2. Answer in units of m.

Answer 1

To find the height of the building, we can use the equations of motion for horizontal and vertical motion.

Step-by-step explanation:

To find the height of the building, we can use the equation for the horizontal motion of the rock. Since the initial vertical velocity is given and the horizontal distance is known, we can find the time it takes for the rock to reach the ground. Then, using the equation for vertical motion, we can find the height of the building.

1. Find the time it takes for the rock to reach the ground using the horizontal distance and the horizontal component of the initial velocity.
2. Use the time from step 1 in the vertical motion equation to find the height of the building.

The height of the building is approximately 20.54 m.