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A stone is dropped from a balloon going up with a uniform velocity of 10 m/s. if the balloon was 40 m high when the stone was dropped, the height of balloon from the ground when the stone hits the ground is (take g = 10 m/s2)
- a)40 m
- b)60 m
- c)80 m
- d)100 m
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A stone is dropped from a balloon going up with a uniform velocity of...
The stone was going up with 10m/s velocity and after that it falls freely under gravity.
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Considering vertically downward as +ve and upward -ve.
S = ut+1/2gt2
S = 40m
u = −10m/s
40 = − 10t + 1/2 × 10 × t2
t2 − 2t − 8 = 0
t2 − 4t + 2t − 8 = 0
t = −2 (no significance in this problem)
t = 4s
Distance covered by balloon in 4 s in upward direction
= 10t = 40m
Total height of balloon = 40 + 40 = 80m
Most Upvoted Answer
A stone is dropped from a balloon going up with a uniform velocity of...
Given data:
- Velocity of the balloon going up = 10 m/s
- Height of the balloon when the stone was dropped = 40 m
- Acceleration due to gravity (g) = 10 m/s²
Analysis:
- When the stone is dropped, it begins to fall under the influence of gravity.
- The balloon continues to move upward with a uniform velocity of 10 m/s.
Calculating time taken by the stone to reach the ground:
- We can use the equation of motion for vertical motion:
h = ut + (1/2)gt²
where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time taken.
- Initially, the stone has zero initial velocity as it is dropped. So, u = 0.
- The height of the balloon from the ground when the stone hits the ground will be the total distance traveled by the stone.
- The height of the balloon from the ground = 40 m
- The height of the stone from the balloon = 40 m (since the stone is dropped from the balloon)
- Total distance traveled by the stone = height of the balloon + height of the stone = 40 m + 40 m = 80 m
- Substituting the values in the equation:
80 = 0 + (1/2)(10)t²
80 = 5t²
t² = 16
t = 4 seconds
Calculating height of the balloon from the ground:
- The height of the balloon from the ground after 4 seconds can be calculated using the equation of motion:
h = ut + (1/2)gt²
where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time taken.
- Initial velocity of the balloon (u) = 10 m/s (as it is going up with a uniform velocity)
- Acceleration due to gravity (g) = 10 m/s²
- Time taken (t) = 4 seconds
- Substituting the values in the equation:
h = 10(4) + (1/2)(10)(4)²
h = 40 + (1/2)(10)(16)
h = 40 + 80
h = 120 m
Conclusion:
- The height of the balloon from the ground when the stone hits the ground is 120 m.
- Therefore, the correct answer is option (c) 80 m.
- Velocity of the balloon going up = 10 m/s
- Height of the balloon when the stone was dropped = 40 m
- Acceleration due to gravity (g) = 10 m/s²
Analysis:
- When the stone is dropped, it begins to fall under the influence of gravity.
- The balloon continues to move upward with a uniform velocity of 10 m/s.
Calculating time taken by the stone to reach the ground:
- We can use the equation of motion for vertical motion:
h = ut + (1/2)gt²
where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time taken.
- Initially, the stone has zero initial velocity as it is dropped. So, u = 0.
- The height of the balloon from the ground when the stone hits the ground will be the total distance traveled by the stone.
- The height of the balloon from the ground = 40 m
- The height of the stone from the balloon = 40 m (since the stone is dropped from the balloon)
- Total distance traveled by the stone = height of the balloon + height of the stone = 40 m + 40 m = 80 m
- Substituting the values in the equation:
80 = 0 + (1/2)(10)t²
80 = 5t²
t² = 16
t = 4 seconds
Calculating height of the balloon from the ground:
- The height of the balloon from the ground after 4 seconds can be calculated using the equation of motion:
h = ut + (1/2)gt²
where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time taken.
- Initial velocity of the balloon (u) = 10 m/s (as it is going up with a uniform velocity)
- Acceleration due to gravity (g) = 10 m/s²
- Time taken (t) = 4 seconds
- Substituting the values in the equation:
h = 10(4) + (1/2)(10)(4)²
h = 40 + (1/2)(10)(16)
h = 40 + 80
h = 120 m
Conclusion:
- The height of the balloon from the ground when the stone hits the ground is 120 m.
- Therefore, the correct answer is option (c) 80 m.
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A stone is dropped from a balloon going up with a uniform velocity of 10 m/s. if the balloon was 40 m high when the stone was dropped, the height of balloon from the ground when the stone hits the ground is (take g = 10 m/s2)a)40 mb)60 mc)80 md)100 mCorrect answer is option 'C'. Can you explain this answer?
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A stone is dropped from a balloon going up with a uniform velocity of 10 m/s. if the balloon was 40 m high when the stone was dropped, the height of balloon from the ground when the stone hits the ground is (take g = 10 m/s2)a)40 mb)60 mc)80 md)100 mCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A stone is dropped from a balloon going up with a uniform velocity of 10 m/s. if the balloon was 40 m high when the stone was dropped, the height of balloon from the ground when the stone hits the ground is (take g = 10 m/s2)a)40 mb)60 mc)80 md)100 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is dropped from a balloon going up with a uniform velocity of 10 m/s. if the balloon was 40 m high when the stone was dropped, the height of balloon from the ground when the stone hits the ground is (take g = 10 m/s2)a)40 mb)60 mc)80 md)100 mCorrect answer is option 'C'. Can you explain this answer?.
A stone is dropped from a balloon going up with a uniform velocity of 10 m/s. if the balloon was 40 m high when the stone was dropped, the height of balloon from the ground when the stone hits the ground is (take g = 10 m/s2)a)40 mb)60 mc)80 md)100 mCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A stone is dropped from a balloon going up with a uniform velocity of 10 m/s. if the balloon was 40 m high when the stone was dropped, the height of balloon from the ground when the stone hits the ground is (take g = 10 m/s2)a)40 mb)60 mc)80 md)100 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is dropped from a balloon going up with a uniform velocity of 10 m/s. if the balloon was 40 m high when the stone was dropped, the height of balloon from the ground when the stone hits the ground is (take g = 10 m/s2)a)40 mb)60 mc)80 md)100 mCorrect answer is option 'C'. Can you explain this answer?.
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