Question

From what height should you drop a ball so that it hits the ground at 40 m/s? How long will it take to hit the ground?

Answer 1

Step-by-step explanation:

It is given that,

A ball hits the ground at 40 m/s

Let h is the height from where you drop a ball. It is based on the conservation of energy as :

`mgh=(1)/(2)mv^2\\\\h=(v^2)/(2g)\\\\\text{Putting all the values in above formula}\\\\h=(40^2)/(2* 9.8)\\\\h=81.63\ m`

It is dropped from a height of 81.63 m.

Let it take t seconds to hit the ground. When it hits the ground, its final speed, v = 0 and u = 40 m/s. So,

`h=ut+(1)/(2)gt^2\\\\h=(1)/(2)gt^2\\\\t=((2h)/(g))^(1/2)\\\\t=((2* 81.63)/(9.8))^(1/2)\\\\t=4.08\ s`

So, it will take 4.08 seconds to hit the ground.