Physic Plz help me!!!!!!!???

Question

A balloon is rising at 10 m/s when its passenger throws a ball straight up at 12 m/s.how much later does the passenger catch the ball?

Answer 1

This is relative motion

Assuming the balloon continues at a constant speed of 10, and that g=10 m/s^2. I will also assume the ball is thrown with a speed of 12 m/s w/r/t the balloon and that the momentum change is negligible due to the ball throw.

then the balloon has
y(t)=10*t

and the ball has
y(t)=(10+12)*t-.5*g*t^2

when they are equal is when the ball is caught
10*t=22*t-5*t^2

note that t=0 is a solution as you would expect. The second root is
t=12/5

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