g You are walking around your neighborhood and you see a child on top of a roof of a building kick a soccer ball. The soccer ball is kicked at 37° from the edge of the building with an initial velocity of 21 m/s and lands 63 meters away from the wall. How tall, in meters, is the building that the child is standing on?

h = 21.5 m

Explanation:

First of all, we define a pair of coordinate axes along the horizontal and vertical direction, calling x-axis to the horizontal and y-axis to the vertical, with the origin in the point where the ball is kicked.Neglecting air resistance, the only influence on the ball once kicked is due to gravity, so the ball is accelerated by the Earth with a constant value of -9.8 m/s2 (assuming the upward direction as positive).So, we can use the kinematic equation for displacement for the vertical direction, as follows:

       

Since the ball is kicked at an angle of 37º from the edge of the building, at an initial velocity of 21 m/s, we can find the horizontal and vertical initial speeds as follows:

       

       

In the horizontal direction, since gravity has no component in this direction, the ball moves at a constant speed, equal to v₀ₓ.Applying the definition of average velocity, since we know the horizontal distance traveled, we can find the total time that the ball was in the air, as follows:

       

Replacing (4) and (3) in (1), we can find the total vertical displacement, which is equal to the height of the building, as follows:

     

⇒ h = -(-21.5m) = 21.5 m