You visited us 5 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Dropping Objects

A balloon sta...

Question

A balloon starts rising upwards with constant acceleration a and after time $t_{0}$ second, a packet is dropped from it which it reaches the ground after t seconds of dropping. Determine the value of t

Open in App

Solution

Analysis of situation: t = 0 is the time when the balloon started rising up. At t = 0, when the packet is dropped, the balloon is moving up with velocity v = 0 + $a t_{0}$ = $a t_{0}$ . Hence, initial velocity of the packet will be $v_{0} = a t_{0}$ (upward). As the balloon has started rising upwards with constant acceleration a, so after $t_{0}$ seconds, its height from the ground is $y_{0} = \frac{1}{2} a t_{0}^{2}$ .
For packet: s = ut - $\frac{1}{2} g t^{2}$
$\Rightarrow$ $- \frac{1}{2} a t_{0}^{2}$ = $a t_{0} t - \frac{1}{2} g t^{2}$ $\Rightarrow$ $g t^{2} - 2 a t_{0} t - a t_{0}^{2} = 0$
Solving the quadratic equation, we get t = $\frac{a t_{0}}{g} [1 + \sqrt{1 + \frac{g}{a}}]$

Suggest Corrections

Similar questions

Q. A balloon starts rising upwards with constant acceleration

15 {m/s}^{2}

and after

10 s

, a packet is dropped from it. The packet reaches the ground after

t_{0} sec

. Determine the value of

t_{0}

(in sec). Take

g = 10 {m/s}^{2}

and

\sqrt{15} = 3.87

Q. A balloon starts from rest is rising upwards with constant acceleration

15 {m/s}^{2}

and after

10 s

, a packet is dropped from it. The packet reaches the ground after

t_{0} sec

. Determine the value of

t_{0}

(in sec). Take

g = 10 {m/s}^{2}

and

\sqrt{15} = 3.87

A balloon starts rising at an acceleration. After some time, a stone is dropped from it. If the stone reaches the ground in the same time in which balloon reached at this point from where stone is dropped, find the acceleration of the balloon:

Q. A balloon starts rising from ground from rest with an upward acceleration

2 m / s^{2}

. Just after

1 s

, a stone is dropped from it. The time taken by stone to strike the ground is nearly

Q. A balloon initially at rest, starts rising from the ground with an acceleration of

2

m / s^{2}

. After

4

s, a stone is dropped from a balloon. In one second of time after the drop, the stone will cover a distance of

(g = 10 m / s^{2})

Join BYJU'S Learning Program

A balloon starts rising upwards with constant acceleration a and after time t0 second, a packet is dropped from it which it reaches the ground after t seconds of dropping. Determine the value of t

A balloon starts rising upwards with constant acceleration a and after time $t_{0}$ second, a packet is dropped from it which it reaches the ground after t seconds of dropping. Determine the value of t