Question

A balloon starts rising from the ground, vertically upwards uniformly at the rate of $1{ms}^{-1}$ . At the end of $4$ seconds, a body was released from the balloon. Calculate the time taken by the released body to reach the ground. Take $g=10{ms}^{-2}$

• A. $4$ s
• B. $1$ s
• C. $6$ s
• D. $3$ s

Answer 1

The correct option is B $1$ s

Height of the balloon after 4 sec $\left(h\right)=vt=4m$

And, velocity$\left(u\right)=-1m/s$ (Taking downward direction as positive)

Now, using 2nd equation of motion $s=ut+\frac{1}{2}{t}^2$

We have,

$h=ut+\frac{g{t}^2}{2}$

$\Rightarrow$$4=(-1)t+\frac{10t^2}{2}$

$\Rightarrow$$4=-t+5t^2$

$\Rightarrow$ $5t^2-t-4=0$

$\Rightarrow (5t+4)(t-1)=0$

$\Rightarrow t=1sec$

Therefore, B is correct option.