Question

A ball is dropped from a balloon going up at a speed of 7 m/s. If the balloon was at a height of 60 m at the time of dropping the ball, how long will the ball take in reaching the ground and what will be its displacement ?

Answer 1

`4.24 s`

Displacement will be `60 m`

Explanation:

When the ball will be dropped,it will have an initial velocity of `7 m/s` upwards,

Now,let it will take time `t` to reach the ground,

so using `s=ut + 1/2 g t^2`

Here, `s= 60 m` (as after going up,it will come down by that distance and will go down by the total displacement of `60 m`) and `,u=-7 m/s` (taking upward direction to be positive)

So,our equation becomes, `60= -7t + 1/2 *10 t^2`

Solving,we get, `t=4.24 s`

ALTERNATIVELY

So,let's calculate the time taken by it to reach the maximum height above the point of release.

using, `v=u-g t`

At its highest point, `v=0`

So, `t= 7/10 s or, 0.7 s`

So,after this it will start falling downwards due to the effect of gravity,so net displacement will be `60 m` ,as it will come down by that distance through which it went upwards after releasing it.

Now to come down by that distance it will take the same amount of time,so to reach its point of release from its highest point,it will take a total of `2*0.7 =1.4 s`

Let,it will take further time `t` to reach the ground after returning to its point of release,

So,using `s=ut + 1/2 g t^2`

Here, `s=60m ,u=7 m/s` (when returning to the point of release,it will gain the same velocity but direction will be reversed.)

So,our equation becomes, `60 = 7t + 1/2 10 t^2`

Solving,we get, `t=2.834 s`

So,total time required to come back to the ground is `1.4+2.834=4.24 s`