Question

A coin is dropped from a balloon going
up with a uniform velocity 12 m/s. If
the ballon was at 81 m high when the
coin was dropped, find its height when
the coin hits the ground. Also,
calculate the time taken by the coin to
hit the ground.​

Answer 1

Answer:

S = V0 t - 1/2 g t^2   where S = distance and V0 = initial velocity

and g = 9.8 m/s^2

-81 = 12 t - 1/2 * 9.8 * t^2     taking up as positive so S is -81 m

4.9 t^2 - 12 t - 81 = 0   or t^2 - 2.45 t - 16.5 = 0

Solving the quadratic for t:  t = 5.47 sec

That is the time for the coin to reach the ground.

Since the balloon continues upward at constant velocity:

H = H0 + V0 t = 81 + 12 * 5.47 = 147 m