A hot air balloon, released from ground, moves up with a constant acceleration of 5 m s − 2 . A stone is released from it at the end of 8s. Find the height (in m) of the stone from the ground, 8s after it is released from the balloon. (Take g = 10 m s − 2 )

Question

A hot air balloon, released from ground, moves up with a constant acceleration of   5  m      s          −      2      . A stone is released from it at the end of 8s. Find the height (in m) of the stone from the ground, 8s after it is released from the balloon. (Take   g  =  10  m      s          −      2      )

Saottah87e · Accepted Answer

The velocity of the stone, when it is released from the balloon is given by, v=u+at and is equal to the velocity of the balloon. Consider the downward direction as advantageous and a replacement,   u  =  0  ,  a  =  −  5  m      s          −      2        ,  t  =  8  v  =  −  5  ×  8  =  −  40  m      s          −      1       The displacement of the stone after 8s is  s  =  u  t  +      1    2    g      t    2   Substituting   s  =  h  ,  u  =  −  40  m      s          −      1        t  =  8  s  ,  g  =  10  m      s          −      2        h  =  −  40  ×  8  +      1    2    ×  10  ×      8    2    h  =  −  320  +  320  =  0 After eight seconds, the stone returns to its original position, which is the height of the balloon above the ground.  s  =  u  t  +      1    2    a      t    2   substitute, u=0  a  =  −  5  m      s          −      2        ,  t  =  8  s  s  =  −      1    2    ×  5  ×  8  ×  8  =  −  5  ×  4  ×  8s=−160 m∴ The height of the balloon from the ground is 160 mThus, the height of the stone from the ground is 160 m.

A hot air balloon, released from ground, moves up with a constant acceleration of 5 ms^(−2). A stone is released from it at the end of 8s. Find the height (in m) of the stone from the ground, 8s after it is released from the balloon. (Take g=10 ms^(−2))

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