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# A balloon starts moving vertically upwards with a uniform acceleration of 1.25 m / s2 After 10 s a stone is dropped from the balloon then find - ( g 10 ms- 2 ) ( 1 ) maximum height from the stone (2 ) the stone time taken to reach the ground

Asked by surabhilakhara7299 14th June 2021, 7:54 AM
Height h reached by baloon after 10 s is determined from the folowing equation

h = (1/2) a t2

where a = 1.25 m/s2 is unifor acceleration of balloon and t is time

h = 0.5 × 1.25 × 10 × 10 = 62.5 m

velocity v of balloon after 10 s , v = a × t = 1.25 × 10 = 12.5 m/s

Hence when the stone is dropped at a height of 62.5 m , it has initial velocity 12.5 m/s upward.

Maximum height H reached by stone from dropping point is determined from the following equation of motion

v2 = u2 - ( 2 g H )

where v = 0 is final velocity because stone reaches zero velocity at maximum height  ,
u is inital velocity of stone and g is acceleration due to gravity.

H = u2 / ( 2 g ) = ( 12.5 × 12.5 ) / ( 2 × 10 ) = 7.8125 m

Maximum height reached by stone from ground = ( 62.5 + 7.8125 ) m = 70.3125 m

Time taken t by stone to reach ground is determined from the following equation

S = u t - [ (1/2) g t2 ]

where S = -62.5 m because stone is dropped at a height of 62.5 m above ground level ,
hence it has to reach this distance backwards.

-62.5 = 12.5 t - [ 0.5 × 10 × t2 ] = 12.5 t - 5 t2

Hence we get a quadratic equation in t ,  5 t2 - 12.5 t - 62.5  = 0

By solving above quadratic equation , we get t = 5 s

Answered by Expert 14th June 2021, 8:37 AM
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Tags: time distance