Motion of a body released from a balloon or a lift:
We will be studying vertical motion of a body when it is released from the ascending balloon or ascending or descending lift that is moving with the uniform velocity or acceleration. In such cases initial velocity of the body is same as velocity of the moving object from which the body is released. The subsequent motion of body will be motion under gravity.
Some Important Results:
Case I: When the lift is ascending with the uniform acceleration of a m/sec2 and after t seconds a body is dropped from it. Then at time when body is dropped.
(i) Initial velocity of body is same as that of the lift and is in the same direction, so, the velocity of body is at m/sec.
(ii) Initial velocity of body relative to the lift = velocity of body - velocity of lift = at - at = 0.
(iii) Acceleration of body = g m/sec2 in downward direction
(iv) Acceleration of lift = a m/sec2 in upward direction
(v) Acceleration of body relative to the lift = Acceleration of the body - Acceleration of lift = g - (-a) = a + g in downward direction.
Case II: When the lift is ascending with the uniform acceleration of a m/sec2 and t seconds a body is thrown vertically upwards having velocity v m/sec. Then at that time
(i) Initial velocity of body = v + velocity of lift = v + at in upward direction
(ii) Initial velocity of body relative to the lift = velocity of body - velocity of lift
= (v + at) -at = v m/sec.
(iii) Acceleration of body relative to the lift in vertically upward direction is (a + g) m/sec2
Case III: When the lift is descending with the uniform acceleration a m/sec2 and after time t a body is dropped from it. Then at that specific time
(i) Velocity of body = velocity of lift = a t m/sec in downward direction
(ii) Initial velocity of body relative to the lift = 0
(iii) Acceleration of body relative to the lift in downward direction = acceleration of body - acceleration of lift = (g - a) m/sec2.
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