20 Physics -- Dynamics

2. A stone is dropped from a balloon going up with a uniform velocity of 5.0 m/s. If the balloon was 50 m high when the stone was dropped, find its height when the stone hits the ground. Take g = 10 m/s2

2. A stone is dropped from a balloon going up with a
uniform velocity of 5.0 m/s. If the balloon was 50 m high
when the stone was dropped, find its height when the
stone hits the ground. Take g = 10 m/s2

Solution

Given:

Height of balloon when stone was dropped (s)= -50 m/s        [since the stone was dropped downwards]

Initial velocity (u) = 5.0 m/s

Acceleration due to gravity (a) =10 m/s2


Using formula,

s = ut + 1/2 * at2

-50 = 5t + 1/2 (-10)t2

-50 = 5t - 5t2

-50 = 5(t - t2)

-50/5 = t - t2

-10 = t - t2

t2- t - 10 = 0

t2 - (3.7 - 2.7) t - 10 = 0

t - 3.7 t + 2.7 t - 10= 0

( t - 3.7 ) ( t + 2.7 ) = 0

Either,

t = 3.7

or,

t = - 2.7

Since time ( t ) can never be negative,

t = 3.7 sec


Height of the balloon when stone hits the ground = 50 + ut

                                                                                       = 50 + 5 * 3.7

                                                                                      = 68.5 m



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