Q. A balloon is at a height of 81m and is ascending upwards with a velocity of 12$ms^{- 1}.$ A body of 2 kg weight is dropped from it. If $g = 10ms^{- 2}$, the body will reach the surface of the earth in
A) 1.5 s
B) 4.025 s
C) 5.4 s
D) 6.75 s
Explanation
(c) $81 = - 12t + \frac{1}{2} \times 10 \times t^{2}$
or $5t^{2} - 12t - 81 = 0$
or $t = \frac{12 \pm \sqrt{144 + 4 \times 5 \times 81}}{2 \times 5}$
$= \frac{12 \pm \ \sqrt{1764}}{10} = \frac{12 \pm 42}{10} = \frac{54}{10} = 5.4s$
[negative sign has been ignored]
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.