Question

A rock climber stands on top of a 60 m-high cliff overhanging a pool of water. He throws two stones vertically downward 1.0 s apart and observes that they cause a single splash. The initial speed of the first stone was 2.4 m/s. In all parts, use the standard sign convention for direction.

How long does it take the first stone to hit the water?

Answer 1

The first stone takes approximately 2.96 seconds to hit the water.

Step-by-step explanation:

To determine how long it takes for the first stone to hit the water, we can use the equation of motion for an object in free fall:

h = (1/2)gt², where h is the height, g is the acceleration due to gravity (9.8 m/s²), and t is the time.

Since the initial velocity of the stone is 2.4 m/s and it is thrown vertically downward, the equation can be rearranged to solve for the time:

60 = (1/2)(9.8)t² + 2.4t

This is a quadratic equation that can be solved for t using the quadratic formula, yielding a positive value of approximately 2.96 seconds. Therefore, it takes about 2.96 seconds for the first stone to hit the water.