Question

A ball is dropped from the top of a building. It falls at a constant rate of 10 miles per hour until it bounces on the sidewalk and then bounces back up at a constant speed until it reaches the top of a building.

a) Is this function linear or non-linear?
b) Explain why.

Answer 1

The motion of the ball is non-linear, and the initial horizontal component of the velocity can be calculated. The vertical component of the velocity just before the ball hits the ground can also be determined. The velocity of the ball just before it hits the ground can be found by combining the horizontal and vertical components.

Step-by-step explanation:

a) The function describing the motion of the ball is non-linear. This is because the motion of the ball involves both horizontal and vertical components, and the velocity changes when the ball bounces on the sidewalk.

b) The initial horizontal component of the velocity can be determined by calculating the distance the ball travels horizontally and the time it takes to reach the ground. Assuming no air resistance, the horizontal component of the velocity remains constant throughout the motion.

c) The vertical component of the velocity just before the ball hits the ground can be determined using the laws of motion and the time it takes for the ball to fall.

d) The velocity of the ball just before it hits the ground can be found by combining the horizontal and vertical components of the velocity. This can be done using vector addition.