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A man in a balloon of 2 m/s relative to the balloon. After what time interval will the ball return to the balloon.
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Let the absolute velocities of the balloon be 'v1' and ball be 'v2'.

  • Givenv1=5 andv2v1=2
  • Hencev25=2
  • v2=7
  • After 't' secs let the ball return to the balloon. Its velocity decreases as the ball moves under gravity, finally ball reaches to the balloon during its upward journey.
  • Displacement of balloon after 't' secs = 5t
  • For ball,u=7 anda=g=9.81m/s2.

s=ut+12at2

s=7t+12(9.81)t2

s=7t12×9.81×t2

s=7t4.905×t2........... equation (1)

  • For ball and balloon to meet each other; Displacement of balloon = Displacement of ball
  • Substitutings=5t in equation (1)
  • Hence5t=7t4.905×t2

4.905t22t=0

t(4.905t2)=0

  • Hencet=0sort=0.4077s
  • The ball will return to the balloon after a total time interval = 0.4077 s.
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