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

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.