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explain

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Asked by adititiwari601 24th June 2022, 9:02 PM
Answered by Expert
Answer:
Let us consider the first stone is dropped when balloon is at a position A . Let vA be its velocity.
 
After 2 seconds the balloon reaches the position B and its speed at B is vB
 
vB = vA + ( a × t )= vA + (0.2 × 2 ) = vA + 0.4    ......................................(1)
 
where a = 0.2 m/s2 is acceleration of balloon
 
In 2 seconds , balloon has travelled a distance h  that is determined from following equation
 
vB2 = vA2 + ( 2 a h )
 
h = ( vB2 - vA2 ) / ( 2 a ) = [ ( vA+0.4 )2 - vA2 ] / ( 2 × 0.2 )
 
h = ( 0.8 vA + 0.16 ) / 0.4  = 2 vA + 0.4  ...................................(2)
 
At position A , when a stone is dropped means , stone moves upwards with speed vA
 
Similarly, At position B , when a stone is dropped means , stone moves upwards with speed vB
 
If it is required to find the distances between two stones 1.5 s after dropping second stone,
then stone dropped at A has travelled 3.5 s and stone dropped at B has travelled only 1.5 s.
 
Let us find the distance by taking positio-A as reference point
 
If hA is the distance travelled by first stone, then
 
hA = ( vA t ) - [ (1/2) g t2 ] = ( 3.5 vA ) - [ 4.9 × 3.5 × 3.5 ]
 
hA = ( 3.5 vA ) - 60.025 
 
If hB is the distance travelled by second stone, then
 
hB = h + ( vB t ) - [ (1/2) g t2 ]
 
Let us substitute h from eqn.(2)  and vB from eqn.(1)
 
hB  = ( 2 vA + 0.4  ) + [ 1.5 ( vA +0.4) ] - [ 4.9 × 1.5 × 1.5 ]
 
hB = ( 3.5 vA ) - 10.025
 
Distance between two stones is calculated as
 
hB - hA = ( 3.5 vA ) - 10.025 - [ ( 3.5 vA ) - 60.025 ]
 
hB - hA = 50 m
 
Answered by Expert 24th June 2022, 11:34 PM
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