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Grade 12th passMechanics

A stone is dropped from a rising balloon at a height of 76 m above ground and reached the ground in 6 s. The velocity of the balloon when the stone was dropped is .............

SAI RAHUL

8 Years agoGrade 12th pass

1 Answer

Arun

8 Years ago

Let Vo = initial upward velocity of stone/balloon.
t = time for stone to reach its max height = Vo/g
max height of stone above ground = H = 1/2gt² + 76 = 0.5(g)(Vo/g)² + 76 = 0.5(Vo)²/g
g = 9.81 m/s²
H = 0.0510(Vo)² + 76
t = 0.10194(Vo)
T = time stone takes to fall distance, H, = √(2H/g) = √[0.102(Vo)² + 152]/9.81 = √[0.0103976(Vo)² + 15.494]
6 = t + T = 0.10194(Vo) + √[0.0103976(Vo)²+15.494]
√[0.0103976(Vo)²+15.494] = 6 - 0.10194(Vo)
0.0103976(Vo)² + 15.494 = 36 - 1.22328(Vo) + 0.010391111(Vo)²
0 = -6.489E-6(Vo)² - 1.22328(Vo) + 20.506
solve quadratic for positive Vo:
Vo = 16.762 ≈ 16.8 m/s (answer)

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