A man in a balloon rising vertically with an acceleration of 4.9 m s-24 releases a stone 2 seconds after the balloon is let go from the ground. The greatest height above the ground reached by the stone is (Take g = 9.8 m s-2)

Question

A man in a balloon rising vertically with an acceleration of 4.9 m s-24 releases a stone 2 seconds after the balloon is let go from the ground. The greatest height above the ground reached by the stone is (Take g = 9.8 m s-2) (A) 14.7 m (B) 19.6 m (C) 9.8 m (D) 24.5 m

Tardigrade Admin · Accepted Answer

Here, a = 4.9 m s-2, t = 2 s, u = 0 S = ut + (1/2)at2 s = 0 +(1/2) ×4.9 ×(2)2 = 9.8 m This is the height from where stone is dropped. Upward velocity of stone when released, upsilon = u + at = 0 + 4.9 × 2 = 9.8 m s-1 The stone will move up till its velocity become zero. From, upsilon2 - u2 = 2as 0 - (9.8)2 = 2(-9.8)s' ∴ s' = 4.9 m Maximum height above the ground = s+s' = 9.8 m + 4.9 m = 14.7

Q. A man in a balloon rising vertically with an acceleration of 4.9ms−24 releases a stone 2 seconds after the balloon is let go from the ground. The greatest height above the ground reached by the stone is (Take g=9.8ms−2)

14.7 m

19.6 m

9.8 m

24.5 m

Q. A man in a balloon rising vertically with an acceleration of $4.9 m s^{- 2} 4$ releases a stone 2 seconds after the balloon is let go from the ground. The greatest height above the ground reached by the stone is (Take $g = 9.8 m s^{- 2}$ )