Question

From a balloon is moving Upwards with velocity $12\, ms^{-1}$. It releases a packet when it is at a height of $65\,m$ from the ground. How much time the packet will take to reach the ground $\left(g=10m/sec^2\right)$

• A. 5 sec
• B. 6 sec
• C. 7 sec
• D. 8 sec

Answer 1

The Correct Option is A

The correct option is(A): 5 sec

Given, \(u= 12\, ms ^{-1}\)
\(S=-65\, m\)
\(\Rightarrow g=-10\, ms ^{-2}\)
We know that, \(s=u t+\frac{1}{2} g t^{2}\)
\(\Rightarrow -65=12 t-\frac{1}{2} \times 10 t^{2}\)
\(-65 =12 t-5 t^{2}\)
\(\Rightarrow 5 t^{2}-12 t-65 =0\)
\(5 t^{2}-25 t+13 t-65 =0\)
\(5 t(t-5)+13(t-5) =0\)
\((5 t+13)(t-5) =0\)
\(\Rightarrow t=-\frac{13}{5}\, s\) or \(t =5\, s\)
Time taken by balloon to reach on ground \(t=5 s\)