balloon is rising vertically up with a velocity of 29 ms−1. A stone is dropped from it and it reaches the ground in 10 seconds. The height of the balloon when the stone was dropped from it, was (g=9.8 ms−2)
Question
balloon is rising vertically up with a velocity of 29 ms−1. A stone is dropped from it and it reaches the ground in 10 seconds. The height of the balloon when the stone was dropped from it, was (g=9.8 ms−2)
Solution
To solve this problem, we need to consider two aspects: the upward motion of the balloon and the downward motion of the stone.
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Upward motion of the balloon: The balloon is moving upward with a velocity of 29 m/s. In the time it takes for the stone to reach the ground (10 seconds), the balloon will have moved further up. The distance it covers is given by the formula d = vt, where v is the velocity and t is the time. So, the balloon moves up a further 29 m/s * 10 s = 290 m.
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Downward motion of the stone: The stone is dropped from the balloon, so it starts with an initial velocity of 0 m/s. It then accelerates downward under gravity. The distance it falls is given by the formula d = 0.5gt^2, where g is the acceleration due to gravity and t is the time. So, the stone falls a distance of 0.5 * 9.8 m/s^2 * (10 s)^2 = 490 m.
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Total height of the balloon: The total height of the balloon when the stone was dropped is the sum of these two distances. So, the height of the balloon was 290 m + 490 m = 780 m.
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