The velocity of the stone, when it is released from the balloon is given by, v=u+at and is equal to the velocity of the balloon. Consider downward direction as positive and substitute,
u=0, a=−5 ms−2, t=8
v=−5×8=−40 ms−1
The displacement of the stone after 8s is
s=ut+12gt2
Substituting s=h, u=−40 ms−1
t=8s, g=10 ms−2
h=−40×8+12×10×82
h=−320+320=0
The stone returns back to the position from where it was released, i.e, the height of the balloon from the ground at the end of 8s.
s=ut+12at2
substitute, u=0
a=−5 ms−2, t=8s
s=−12×5×8×8=−5×4×8
s=−160 m
∴ The height of the balloon from the ground is 160 m
Thus, the height of the stone from the ground is 160 m.