A balloon is moving vertically upward with speed 10 m/s and has a constant upward acceleration of 2 m/ $s^2.$ When the balloon is 80 m above the ground, a stone is released from it. Neglect air resistance and take g = 10 m/ $s^2.$ The time taken by the stone to reach the ground after release is:
Options

Question

A balloon is moving vertically upward with speed 10 m/s and has a constant upward acceleration of 2 m/ $s^2.$ When the balloon is 80 m above the ground, a stone is released from it. Neglect air resistance and take g = 10 m/ $s^2.$ The time taken by the stone to reach the ground after release is:

Options

G1 Physics · Accepted Answer

At the instant of release, the stone has the balloon's instantaneous velocity 10 m/s upward. After release, the balloon's acceleration no longer affects the stone; only gravity acts. Taking upward positive: 0 = 80 + 10t - 5t^2. Thus t^2 - 2t - 16 = 0, so t = 1 + sqrt(17) s. Hence option B is correct.

A balloon is moving vertically upward with speed 10 m/s and has a constant upward acceleration of 2 m/s^2. When the balloon is 80 m above the ground, a stone is released from it. Neglect air resistance and take g = 10 m/s^2. The time taken by the stone to reach the ground after release is: