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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
Answered by Expert
Answer:
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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