Question

A balloon starts rising from the ground with acceleration of 1.25 msâ»Â². After 8 s a stone is released from the balloon. How much time will it take to reach the ground?
(A) 2 s
(B) 4 s
(C) 6 s
(D) 10 s

Answer 1

Answer:

it take 4 sec to reach the ground

Explanation:

A balloon starts rising from the ground with acceleration of 1.25 m/s²

Velocity upward after 8 sec is given by V = U + at

= 0 + 1.25 * 8

= 10 m/s

Distance Covered = Ut + (1/2)at² = 0 + (1/2)*1.25 * 8² =  40 m

Stone is dropped from 40 m height at Velocity = 10 m/s Upward

Velocity = -10 m/s²

a =  10 m/s²

Distance to be covered = 40 m

40 = -10t + (1/2)10t²

=> 40 = -10t + 5t²

=> 8 = -2t + t²

=> t² - 2t - 8 =0

=> t² - 4t + 2t - 8 = 0

=> t(t  - 4) + 2(t - 4) = 0

=> (t + 2)(t - 4) = 0

=> t = 4

it take 4 sec to reach the ground

Answer 2

First we need to find the height at which the stone is dropped.

s=ut+1/2at^2

s=0+1/2×1.25×8^2

s=1.25×64/2

s=40m

Now we will find the time it takes to go up and come back to height 40m. The initial velocity will be 1.25×8=10

v=u+at

0=10+(-10t)

-10=-10t

1=t

Therefore time to go up and come back to point where stone was dropped is equal to 1×2=2

Now we find the time it takes to go from 40m to 0m.

s=ut+1/2at^2

40=10t+1/2(10t^2)

40=5(2t+t^2)

40/5=2t+t^2

8=2t+t^2

t=2

Therefore total time taken is equal to 2+2=4=t.

I hope you find this useful.