Motion in one dimension
A balloon starts from ground and moves vertically upwards with an acceleration of 2m/s. After 5m/s,a stone is released from the balloon. Find the time taken by the stone to reach the ground.
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Time taken for balloon to reach 5m/s = v/a = 5/10 = 0.5s
Distance travelled by balloon in 0.5s = 0.5at^2 = 0.5*9.8*(0.5)^2 = 1.225m
Velocity of stone when it hits the ground = sqrt(u^2 + 2gH) = sqrt(25 + 2*9.8*1.225) ≈ 7m/s
Time taken by stone reach its initial position of fall = 2u/g = 2*5/9.8 ≈ 1s
Further time taken by stone to reach ground = (v - u)/a = (7 - 5)/9.8 ≈ 0.2s
Total time taken = 1.2s
Distance travelled by balloon in 0.5s = 0.5at^2 = 0.5*9.8*(0.5)^2 = 1.225m
Velocity of stone when it hits the ground = sqrt(u^2 + 2gH) = sqrt(25 + 2*9.8*1.225) ≈ 7m/s
Time taken by stone reach its initial position of fall = 2u/g = 2*5/9.8 ≈ 1s
Further time taken by stone to reach ground = (v - u)/a = (7 - 5)/9.8 ≈ 0.2s
Total time taken = 1.2s
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