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

Answer:

$v=-1.46 \ m/s$

Step-by-step 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,

$v_{final}^2 - v_{initial}^2 =2\times a\times displacement$   .....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 .

$v_{final}^2-0^2 =2\times 9.8 \times 11$

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

But as we know direction of velocity is downward.

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

where negative sign indicates its direction is downward.