Question

A balloon rises vertically upward with a constant
velocity of 30 m/s. When the balloon is at a height
of 80 m, a stone is dropped from it. The time taken
by stone to reach the ground is (Take g = 10 ms-2)​

Answer 1

Answer:

8 s

Explanation:

1)  Since, speed of balloon is constant .

When stone is dropped at 80 m, its velocity is 30m/s in upward direction.

Convention : Upward Direction : +

                   Downward direction : -

So, To get time taken to reach the ground we need,

u=+30m/s

$S_y = -80 m\\a= -10 m/s^2$

Then,

Using Newton's equation of motion,

$S_y=u_y+\frac{1}{2}at^2\\ \\=>-80=30t+0.5*(-10)t^2\\ \\=> t^2-6t-16=0\\ \\=>(t-8)(t+2)=0\\ \\=>t = 8s$

Hence,

Time taken to reach the ground is 8s .

Answer 2

SOLUTION.

As balloon rises upwards with constant speed so when a stone is released from it than the stone has some velocity in upward direction of same magnitude.

Time taken to nullify initial velocity of stone

u = 30m/sec

v = 0

v = u - gt

0 = 30 - 10t

t = 3sec.....(1)

Distance traveled by the stone in this time interval.

v² = u² - 2gh

0 = 900 - 20h

h = 45m

TOTAL HEIGHT = 125m

Time taken to cover this height.

u = 0

H = ut + (1/2)gt²

125 = 0×t + (1/2)×10×t²

125 = 5t²

t² = 25

Time = 5sec.....(2)

Total time = (1) + (2)

Total time = 8sec

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