A balloon is rising vertically upwards with a velocity of $10\,\text{m s}^{-1}$. When the balloon is at a height of $40\,\text{m}$ from the ground, a stone is dropped from it. The time taken by the stone to reach the ground is (Take $g=10\,\text{m s}^{-2}$).

Question

A body starts from rest and moves with constant acceleration. If it covers a distance of $ 40 \, \text{m} $ in 4 seconds, then its acceleration is:

Answer 1

Concept: Stone released with upward velocity $u=10$ m/s from $y_0=40$ m. Use $y = y_0 + ut + \frac12 at^2$ with $a=-g=-10$. Solve $0=40+10t-5t^2$.

Step 1: $t^2 - 2t - 8 = 0 \Rightarrow (t-4)(t+2)=0 \Rightarrow t=4$ s (positive).

Step 2: Write the final answer. $\boxed{4\,\text{s}}$

A balloon is rising vertically upwards with a velocity of \(10\,\text{m s}^{-1}\). When the balloon is at a height of \(40\,\text{m}\) from the ground, a stone is dropped from it. The time taken by the stone to reach the ground is (Take \(g=10\,\text{m s}^{-2}\)).

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The Correct Option is D

Solution and Explanation

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