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a stone A is thrown vertically upward with speed U and another stone B is thrown vertically downward with same speed U from a height h. The time taken by stone A and B to reach the ground are 16 second and 4 seconds respectively. The time taken by another stone to reach the ground after it has been dropped from height H is(take g=10m/s^2)

a stone A is thrown vertically upward with speed U and another stone B is thrown vertically downward with same speed U from a height h. The time taken by stone A and B to reach the ground are 16 second and 4 seconds respectively. The time taken by another stone to reach the ground after it has been dropped from height H is(take g=10m/s^2)

Grade:9

1 Answers

Arun
25763 Points
3 years ago
Given, time taken by stone A is 16s 
Initial speed = u 
Time taken by stone B is 4s
Initial speed = u 
final velocity = 0 
V = u+at
0 = u+ 10*40
Therefore u for second stone is -40m/s
As the height is same for both the stones, 
S = u*16+1/2*-10*16*16 for stone 1 ----(1)
S = -40*4+1/2*10*4*4 ----- (2)
Now, equating eqn. 1 and 2
u*16+1/2*-10*16*16 = -40*4+1/2*10*4*4
u = 75m/s for stone 2
Now, s = 75*16+1/2*-10*16*16
S = -80m
Now for stone 3,
v = 0, 
v^2 - u^2 = 2as
0 - u^2 = 2*10*-80
Therefore u = 400m/s
Now, v = u+at
0 = 400+10*t
Therefore time taken by third stone is 40sec

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