a stone is dropped from a balloon rising upwards with a velocity of 16m/s .the stone reaches the ground in 4s.calculate the height of the balloon when the stone was dropped
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At the time of dropping the stone, let the height of balloon (and stone) be H. Let that be t = 0 sec.
At t = 0 sec, the stone is also traveling with a speed of 16 m/s upwards.
The additional height it reaches = h. Let g = 10 m/s²
v² = u² - 2 g h => h = 16²/(2*10) = 12.8 m
Time taken to reach the maximum height = t1
v = u - g t => t1 = 16/10 = 1.6 sec
Time taken to fall the height of H + 12.8 m = t2 = 4 s - 1.6s = 2.4 s
So s = u t + 1/2 g t² => H + 12.8 = 0 + 1/2 * 10 * 2.4²
H = 28.8 - 12.8 = 16.0 m
At t = 0 sec, the stone is also traveling with a speed of 16 m/s upwards.
The additional height it reaches = h. Let g = 10 m/s²
v² = u² - 2 g h => h = 16²/(2*10) = 12.8 m
Time taken to reach the maximum height = t1
v = u - g t => t1 = 16/10 = 1.6 sec
Time taken to fall the height of H + 12.8 m = t2 = 4 s - 1.6s = 2.4 s
So s = u t + 1/2 g t² => H + 12.8 = 0 + 1/2 * 10 * 2.4²
H = 28.8 - 12.8 = 16.0 m
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