Question

A balloon starts rising from the ground with an acceleration of 1.25 m/s2. After 8 s, a stone is released from the balloon. The stone will, after release from the balloon,​

Answer 1

Explanation:

Steps:

1) Initially,

Initial velocity, u = 0m/s

acceleration, a =1.25 m/s^2

Velocity of balloon after 8 s, v = u +at

=> v = 0 + 1.25 * 8 = 10m/s

2) Displacement of balloon in 8 s,

\begin{lgathered}s = ut + \frac{1}{2} a {t}^{2} \\ = > 0 + \frac{1}{2} \times 1.25 \times {8}^{2} = 40m\end{lgathered}

s=ut+

2

1

at

2

=>0+

2

1

×1.25×8

2

=40m

3) After t = 8s, a stone is dropped.

Initial velocity of stone at time of fall is same as that of balloon at that time :

That is velocity of stone,when it is dropped is 10m/s upward.

Initial velocity, u = 10m/s

Displacement, s = -40m ( - means downward)

Balloon is left.

Acceleration, a = -10 m/s^2

So, time taken by stone to reach the

\begin{lgathered}s = ut + \frac{1}{2} a {t}^{2} \\ - 40 = 10t + \frac{1}{2} \times( - 10) \times {t}^{2} \\ = > {t}^{2} - 2t - 8 = 0 \\ = > (t + 2)(t - 4) = 0 \\\end{lgathered}

s=ut+

2

1

at

2

−40=10t+

2

1

×(−10)×t

2

=>t

2

−2t−8=0

=>(t+2)(t−4)=0

t = 4 s, t = -2 (rejected)

Therefore, Stone will take 4 seconds to reach the ground after being dropped from balloon at height h =40m from ground.