Question

A man stands on the roof of a building of height 13.0m and throws a rock with a velocity of magnitude 33.0m/s at an angle of 25.3(degree) above the horizontal. You can ignore air resistance.Calculate the maximum height above the roof reached by the rock.

Answer 1

The maximum height above the roof reached by the rock is approximately 16.8 meters.

Step-by-step explanation:

To calculate the maximum height reached by the rock, we need to consider the vertical motion of the rock. We can break the initial velocity of the rock into its vertical and horizontal components. The vertical component is given by the initial velocity (33 m/s) multiplied by the sine of the launch angle (25.3 degrees). Using this component, we can calculate the time it takes for the rock to reach its peak height using the formula:

t = (Vf - Vi) / a

where Vf = 0 m/s (at the peak), Vi is the vertical component of the initial velocity, and a is the acceleration due to gravity (-9.8 m/s^2). Once we have the time, we can calculate the maximum height reached by the rock using the formula:

h = Vi * t + 0.5 * a * t^2

Using these calculations, the maximum height above the roof reached by the rock is approximately 16.8 meters.