A light is attached to the wall of a building 64 feet above
the ground. A ball is dropped from the same height, but 20
feet away from the side of the building. The height y of the
ball at time t is given by y(t) = 64 − 16t
2
. How fast is the
shadow of the ball moving along the ground after 1 second?
To find the speed at which the shadow of the ball is moving along the ground after 1 second, we need to determine the rate of change of the horizontal distance between the ball and the wall at that specific time.
In this case, the ball is dropped 20 feet away from the side of the building. Since it is dropped vertically, the horizontal distance between the ball and the building remains constant throughout the ball's fall.
Therefore, the shadow of the ball will move at a constant speed of 20 feet per second along the ground, regardless of the time.