Question

A balloon is rising vertically up with a velocity of $29{\mathrm{ms}}^{-1}$. A stone is dropped from it and it reaches the ground in $10\mathrm{s}$. The height of the balloon when the stone was dropped from it is ( take,$\mathrm{g}=9.8{\mathrm{ms}}^{-2}$)

• A. $400\mathrm{m}$
• B. $150\mathrm{m}$
• C. $100\mathrm{m}$
• D. $200\mathrm{m}$

Answer 1

The correct option is D

$200\mathrm{m}$

Step 1: Given data

Initial velocity of stone, $\mathrm{u}=29{\mathrm{ms}}^{-1}$

Time taken to reach the ground, $\mathrm{t}=10\mathrm{s}$

Acceleration, $\mathrm{a}=\mathrm{g}=-9.8{\mathrm{ms}}^{-2}(\because \mathrm{direction}\mathrm{of}\mathrm{stone}\mathrm{and}\mathrm{balloon}\mathrm{are}\mathrm{opposite})$

Let height of balloon is given by, $\mathrm{h}$

Step 2: Calculating the height of balloon

By using the equation of motion we can calculate the height as below:

$$\begin{gathered} \mathrm{S}=\mathrm{ut}+\frac{1}{2}{\mathrm{at}}^2 \\ \Rightarrow -\mathrm{h}=29\times 10+\frac{1}{2}\times \left(-9.8\right)\times {\left(10\right)}^2 \\ \Rightarrow -\mathrm{h}=290-490 \\ \Rightarrow -\mathrm{h}=-200 \\ \Rightarrow \mathrm{h}=200\mathrm{m} \end{gathered}$$

Therefore height of a balloon is equal to $200\mathrm{m}$

Hence, option(D) is correct answer.