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from a balloon rising vertically upwards at 5m /s a stone is thrown up at 10m/s relative to the balloon. its velocity with respect to ground after 2 second is
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from a balloon rising vertically upwards at 5m /s a stone is thrown up...
Problem:

A balloon is rising vertically upwards at 5m/s. A stone is thrown up at 10m/s relative to the balloon. Find its velocity with respect to the ground after 2 seconds.


Solution:

Let's consider the upward direction as positive and downward direction as negative.


Velocity of the balloon:


  • Velocity of the balloon = 5 m/s (given)



Velocity of the stone:


  • Velocity of the stone relative to the balloon = 10 m/s (given)

  • Since the stone is thrown upward, its initial velocity is positive.

  • The acceleration due to gravity is acting in the downward direction and its value is 9.8 m/s².

  • After 2 seconds, the stone reaches its maximum height and starts falling back.

  • Therefore, the velocity of the stone after 2 seconds = initial velocity - acceleration due to gravity × time

  • Velocity of the stone after 2 seconds = 10 - 9.8 × 2 = -8.6 m/s

  • Here, the negative sign indicates that the velocity of the stone is in the downward direction.



Velocity of the stone with respect to the ground:


  • Velocity of the stone with respect to the ground = Velocity of the balloon + Velocity of the stone relative to the balloon

  • Velocity of the stone with respect to the ground = 5 + (-8.6) = -3.6 m/s

  • Here, the negative sign indicates that the velocity of the stone is in the downward direction with respect to the ground.



Answer:

The velocity of the stone with respect to the ground after 2 seconds is -3.6 m/s.
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