Question

a ball dropped from a balloon at rest clear the tower 81 m high during the last quarter second of its journey find the height of the balloon and the velocity of the body when it reaches the ground

Answer 1



 

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A ball dropped from a balloon at rest clears a tower  81m high during the last quater second of its journey. Find the height of the balloon and the velocity of the body when it reaches the ground.


WHAT IT MEANS- LAST QUATER SECOND OF ITS JOURNEY.

5 years ago

Answers : (1)

The last quarter of the jouney menas 1/4th of the total time it requires in its total journey.

Let total time be 4t, u = 0.

So, v at 3t = 3gt, and at 4t = 4gt.

by v² = u² + 2as,

16g²t² = 9g²t² + 2g(81)

7g²t² = 162g

7gt2 = 162

t² = 162 / 7g

t = 1.5 sec.

but time is 4t = 6 sec.

So velocity on reaching = 4gt = 58.8 m/s

With this velocity, height of fall = 2t(58.8) = 705.6m

Answer 2

Answer:

In this case, we know from equation (1) that 81 = 0.25u + 4.905(0.25^2), so

u = 322.774m/s

Then from equation (4) 81 = (322.774 + v)0.25/2, or

v = 325.224m/s is the velocity at impact

Finally, from equation (2), 325.224^2 = 0 + 2(9.81)s, or

s = 5390.96m

The balloon was at a height of 5390.96m