Question

How long will the ball be in the air if the cliff is 120 m tall and the ball falls to the base of the cliff?

Answer 1

For 5 s the ball will remain in air.

Step-by-step explanation:

Given:

Displacement of the ball is equal to height of cliff,
`S=120\ m`

Acceleration of the ball is acceleration due to gravity,
`a=g=9.8\ m/s^2`

Assuming the ball is dropped from the top.

Hence, initial velocity of the ball is,
`u=0\ m/s`

Let 't' be the time the ball takes to reach the base of cliff.

Now, we have to use the Newton's equations of motion that relates displacement, initial velocity, acceleration and time.

So, we use the following equation of motion:

`S=ut+(1)/(2)at^2`

Plug in the given values and solve for 't'. This gives,

`120=0+(1)/(2)(9.8)t^2\\120=4.9t^2\\(120)/(4.9)=t^2\\t^2\approx25\\t=√(25)=5\ s`

Therefore, the time till the ball is in air is approximately 5 s.