Question

A ball rolls off a cliff at 42.5 m/s. It takes 9.2 seconds for the ball to hit the ground.

i) Calculate the height of the cliff.
ii) What is the horizontal distance from the base of the cliff?

Answer 1

The height of the cliff is 414.09 meters, and the horizontal distance from the base of the cliff is 390.8 meters.

Step-by-step explanation:

To calculate the height of a cliff from which a ball rolls off at a constant velocity and takes a given time to reach the ground, we can use the kinematic equations for free fall motion under the influence of gravity. We are given an initial horizontal velocity of 42.5 m/s and a fall time of 9.2 seconds. We can ignore air resistance and other factors in our calculation.

The height (h) of the cliff can be determined using the formula for vertical displacement: h = ½ gt², where g is the acceleration due to gravity (9.81 m/s²) and t is the time (9.2 s).

To calculate the horizontal distance (d) from the base of the cliff, we use the formula d = vt, where v is the horizontal velocity and t is the time.

Calculations:

1. Height of the cliff: h = ½ × 9.81 m/s² × (9.2 s)² = 414.09 m
2. Horizontal distance: d = 42.5 m/s × 9.2 s = 390.8 m