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Motion in Straight Line

Free fall motion

A balloon is going up with a uniform speed 20 {~m} / {s}. It w

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Solving time: 3 mins

A balloon is going up with a uniform speed $20 m / s$ . It was at a height of $100 m$ from ground, when a stone is dropped from its basket. Find the time taken by the stone to reach the ground and the height of the balloon from the ground, when stone hits the ground. (Take $g = 10 m / s^{2}$ )

Views: 5,925 students

Updated on: Sep 29, 2022

Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

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James Discussed

A balloon is going up with a uniform speed

20 m / s

. It was at a height of

100 m

from ground, when a stone is dropped from its basket. Find the time taken by the stone to reach the ground and the height of the balloon from the ground, when stone hits the ground. (Take

g = 10 m / s^{2}

)

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

As balloon is going up, when stone is dropped, it will also has the same upward speed of

20 m / s

. So it will first go up retarded by gravity and fall back towards ground. The practical situation is shown in figure-
Solution Image

Here to find time we use second speed equation for free fall motion

h = u t - \frac{1}{2} g t^{2}

From figure, here we take

u = 20 m / s

and

h = - 100 m

.
We have

- 100 = 20 t - \frac{1}{2} (10) t^{2}

Solving, it gives

t = 6.89 s

t = - 2.89 s

Thus stone will take

6.89

s to reach the ground and it will follow the path shown in figure by dotted line.
In this duration, balloon ascends a height

= 20 \times 6.89 = 137.8 m

Height of balloon from ground at the instant, stone hitting the ground is

= 100 + 137.8 = 237.8 m

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Question Text	A balloon is going up with a uniform speed $20 m / s$ . It was at a height of $100 m$ from ground, when a stone is dropped from its basket. Find the time taken by the stone to reach the ground and the height of the balloon from the ground, when stone hits the ground. (Take $g = 10 m / s^{2}$ )
Updated On	Sep 29, 2022
Topic	Motion in Straight Line
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 14
Upvotes	1359
Avg. Video Duration	7 min

A balloon is going up with a uniform speed $20 m / s$ . It was at a height of $100 m$ from ground, when a stone is dropped from its basket. Find the time taken by the stone to reach the ground and the height of the balloon from the ground, when stone hits the ground. (Take $g = 10 m / s^{2}$ )

Text solutionVerified

Filo tutor solutions (14)

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A balloon is going up with a uniform speed 20 m/s. It was at a height of 100 m from ground, when a stone is dropped from its basket. Find the time taken by the stone to reach the ground and the height of the balloon from the ground, when stone hits the ground. (Take g=10 m/s2 )

Text solutionVerified

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A balloon is going up with a uniform speed $20 m / s$ . It was at a height of $100 m$ from ground, when a stone is dropped from its basket. Find the time taken by the stone to reach the ground and the height of the balloon from the ground, when stone hits the ground. (Take $g = 10 m / s^{2}$ )