Question

You are trying to find out how high you have to pitch a water balloon in order for it to burst when it hits the ground. You discover that the balloon bursts when you have pitched it to a height of 16 m. With what velocity did the balloon hit the ground? The acceleration of gravity is 9.8 m/s 2 . The positive direction is up, so the velocity when it hits is negative. Answer in units of m/s.

Answer 1

Answer: -17.7 m/s

The maximum height achieved by balloon,
`s=16 m`

The instantaneous velocity at the maximum height,
`u=0`

The balloon free falls under gravity,
`a=9.8m/s^2`

Using the equation of motion:

`v^2-u^2=2as`

where,
`v` is the final velocity,
`u` is the initial velocity,
`a` is the acceleration and
`s` is the distance covered.

Substitute the values:

`v^2-0=2* 9.8 m/s^2 * 16 m`

`\Rightarrow v=√(313.6 m^2/s^2)=\pm 17.7 m/s`

We will consider only the negative value, as the positive direction is considered upwards.