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 in units of m/s.

Answer 1

-14.68 m/s

Step-by-step explanation:

You are given the height of the balloon that it is "dropped": 11 m. Since the final velocity of a projectile is 0 m/s at the top of its flight, we can say that the initial velocity is 0 m/s and the displacement is -11 m (the balloon "starts" at the top of its trajectory).

We know the acceleration of the balloon is -9.8 m/s².

Use this kinematic equation that relates all four variables (displacement, initial velocity, final velocity, acceleration):

• v² = v₀² + 2aΔx

Substitute known variables into the equation.

• v² = 0² + 2(-9.8)(-11)
• v² = 215.6
• v = √215.6
• v = 14.68332387
• v = 14.68

Since the positive direction is up, the velocity when it hits the ground must be negative. The balloon hits the ground with a velocity of -14.68 m/s.