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 11 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 1

`v=-1.46 \ m/s`

Explanation:

So, as balloon reaches its maximum height i.e. 11 m , its velocity become 0.

Therefore,
`v_(top)=0 \ m/s`.

It is given that acceleration due to gravity should be taken as ,
`g=-9.8 \ m/s^2`.(because it direction is down)

Now it is also given that upward direction is positive and downward direction is negative. So velocity should be negative.

Using equation of motion,

`v_(final)^2 - v_(initial)^2 =2* a* displacement` .....eqn 1.

where , displacement = -11 m(because it displace towards down) and
`a=g=-9.8\ m/s^2`

Putting these values in eqn 1 .

`v_(final)^2-0^2 =2* 9.8 * 11`

`v = \pm1.46 m/s.`

But as we know direction of velocity is downward.

Therefore,
`v=-1.46 \ m/s`

where negative sign indicates its direction is downward.