Question

A balloon is at a height of 81 m and is ascending upwards with a velocity of $12\frac{m}{s}$. A body of 2kg weight is dropped from it. If $g=10\frac{m}{s^2}$, the body will reach the surface of the earth in

A. 4.025 s

B. 5.4 s

C. 6.75 s

D. 1.5 s

• A. 1.5 s
• B. 4.025 s
• C. 5.4 s
• D. 6.75 s

Answer 1

Answer: (C)

Given,

Height = $h=81m$

Initial velocity = $u=12\frac{m}{s}$

Mass = $m=2kg$

Acceleration due to gravity = $g=-10\frac{m}{s^2}$

Using the second equation of motion, $s=ut+\frac{1}{2}a{t}^2$, we get

$-81=12t+\frac{1}{2}(-10)t^2$ $\Rightarrow 5t^2-12t-81$

(Since displacement is in the downward direcion, it is taken as negative)

On solving we get, $t=5.4s$ and $t=-3s$

Thus, the body will reach the surface of the earth in 5.4 seconds.

Hence option (b) is correct.

Remember time cannot be negative.