Question

A balloon starts rising from rest from the ground with an acceleration of 1.25 m/s2. After 8s, a stone is released from the balloon. The stone will. (a)cover a distance of 40m (b)have a displacement of 50 m (c)each the ground in 4s (d)begin to move down after being released

Answer 1

After 8 s, both the balloon and the stone have upward velocity of
v = (1.25 m/s^2)*(8 s) = 10 m/s
Both the balloon and the stone would have traveled upward by a height of
h = (1/2)*(1.25 m/s^2)*(8 s)^2 = 40 m

When the stone is dropped, it will
(a) have an initial upward speed of  10 m/s,
(b) it will be 40 m above ground,
(c) the time for it to reach the ground is given by
    (10 m/s)t - (1/2)*(9.81 m/s^2)t^2 = -40
    4.9t^2 - 10t - 40 =0
    Use the quadratic formula to obtain t = 4.054 s
(d) it will travel a distance upward, s, given by
    0 = 10^2 - 2(9.8)s => s = 5.1 m
    The stone will attain a height of 45.1 m aboe ground.

Answer:
c. The stone will reach the ground in 4 s.