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A man in a balloon, throws a stone downwards with a speed of 5 m/s with respect to the balloon. The balloon is moving upwards with constant acceleration of 5 m/s2. Then velocity of the stone relative to the man after 2 second is
- a)10 m/s
- b)30 m/s
- c)15 m/s
- d)35 m/s
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A man in a balloon, throws a stone downwards with a speed of 5 m/s wi...
Initial speed u = 5 m/s
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After 2 second v = u + gt = 5 + 10 × 20 = 25 m/s
& the speed of balloon after 2 second will v = 1/2 a(2)2 = 2a = 2 × 5 =10 m/s
Balloon upward
Stone downward
So opposite so speed should be added so relative speed = 25 + 10 = 35 m/s
Most Upvoted Answer
A man in a balloon, throws a stone downwards with a speed of 5 m/s wi...
Given:
- Stone is thrown downwards with a speed of 5 m/s with respect to the balloon.
- The balloon is moving upwards with a constant acceleration of 5 m/s^2.
To Find:
Velocity of the stone relative to the man after 2 seconds.
Explanation:
Step 1: Analyzing the motion of the balloon and the stone
- The stone is thrown downwards with a speed of 5 m/s.
- The balloon is moving upwards with a constant acceleration of 5 m/s^2.
Step 2: Understanding relative velocity
- Relative velocity is the vector difference between the velocities of two objects.
- In this case, we need to find the velocity of the stone relative to the man.
Step 3: Calculating the velocity of the balloon after 2 seconds
- The balloon has an initial velocity of 0 m/s.
- The acceleration of the balloon is 5 m/s^2.
- Using the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
- Plugging in the values, we get v = 0 + (5)(2) = 10 m/s.
Step 4: Calculating the velocity of the stone relative to the ground
- The stone is thrown downwards with a speed of 5 m/s.
- The balloon is moving upwards with a velocity of 10 m/s after 2 seconds.
- The velocity of the stone relative to the ground is the vector difference between the velocity of the stone and the velocity of the balloon.
- Therefore, the velocity of the stone relative to the ground is 5 m/s - 10 m/s = -5 m/s.
Step 5: Calculating the velocity of the stone relative to the man
- The velocity of the stone relative to the man is the vector sum of the velocity of the stone relative to the ground and the velocity of the balloon relative to the man.
- Since the stone is thrown downwards and the balloon is moving upwards, their velocities are in opposite directions.
- Therefore, the velocity of the stone relative to the man is -5 m/s + 10 m/s = 5 m/s.
Step 6: Conclusion
The velocity of the stone relative to the man after 2 seconds is 5 m/s.
Therefore, the correct answer is option D) 35 m/s.
- Stone is thrown downwards with a speed of 5 m/s with respect to the balloon.
- The balloon is moving upwards with a constant acceleration of 5 m/s^2.
To Find:
Velocity of the stone relative to the man after 2 seconds.
Explanation:
Step 1: Analyzing the motion of the balloon and the stone
- The stone is thrown downwards with a speed of 5 m/s.
- The balloon is moving upwards with a constant acceleration of 5 m/s^2.
Step 2: Understanding relative velocity
- Relative velocity is the vector difference between the velocities of two objects.
- In this case, we need to find the velocity of the stone relative to the man.
Step 3: Calculating the velocity of the balloon after 2 seconds
- The balloon has an initial velocity of 0 m/s.
- The acceleration of the balloon is 5 m/s^2.
- Using the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
- Plugging in the values, we get v = 0 + (5)(2) = 10 m/s.
Step 4: Calculating the velocity of the stone relative to the ground
- The stone is thrown downwards with a speed of 5 m/s.
- The balloon is moving upwards with a velocity of 10 m/s after 2 seconds.
- The velocity of the stone relative to the ground is the vector difference between the velocity of the stone and the velocity of the balloon.
- Therefore, the velocity of the stone relative to the ground is 5 m/s - 10 m/s = -5 m/s.
Step 5: Calculating the velocity of the stone relative to the man
- The velocity of the stone relative to the man is the vector sum of the velocity of the stone relative to the ground and the velocity of the balloon relative to the man.
- Since the stone is thrown downwards and the balloon is moving upwards, their velocities are in opposite directions.
- Therefore, the velocity of the stone relative to the man is -5 m/s + 10 m/s = 5 m/s.
Step 6: Conclusion
The velocity of the stone relative to the man after 2 seconds is 5 m/s.
Therefore, the correct answer is option D) 35 m/s.
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A man in a balloon, throws a stone downwards with a speed of 5 m/s with respect to the balloon. The balloon is moving upwards with constant acceleration of 5 m/s2. Then velocity of the stone relative to the man after 2 second isa)10 m/sb)30 m/sc)15 m/sd)35 m/sCorrect answer is option 'D'. Can you explain this answer?
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