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Question: A balloon is at a height of 81 m and is ascending upwards with a velocity of \(12m/s.\) A body of 2 ...

A balloon is at a height of 81 m and is ascending upwards with a velocity of 12m/s.12m/s. A body of 2 kg weight is dropped from it. If g=10m/s2,g = 10m/s^{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

Answer

5.4 s

Explanation

Solution

As the balloon is going up we will take initial velocity of falling body =−12m/s,h=81m,g=+10m/s2= - 12m/s,\mathbf{h = 81m,}\mathbf{g = + 10m/}\mathbf{s}^{\mathbf{2}}

By applying h=ut+12gt2h = ut + \frac{1}{2}gt^{2}; 81=−12t+12(10)t281 = - 12t + \frac{1}{2}(10)t^{2}

⇒ 5t2−12t−81=05t^{2} - 12t - 81 = 0

⇒ t=12±144+162010t = \frac{12 \pm \sqrt{144 + 1620}}{10} =12±176410≈5.4sec.= \frac{12 \pm \sqrt{1764}}{10} \approx 5.4sec.