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Question
A ball is dropped from a pole of height 100m and simultaneously a stone is thrown upwards, they meet at a point 55m above the ground. The velocity with which the stone must be thrown should equal to
A ball is dropped from a pole of height 100m and simultaneously a stone is thrown upwards, they meet at a point 55m above the ground. The velocity with which the stone must be thrown should equal to
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Solution
The correct option is A 100/3 m/s
Let us take the velocity with which the stone is thrown is equal to 'u' m/s. Now the time 't' at which they meet is actually the time in which the ball covers a distance of (100 - 55) = 45m. SO, taking upward direction as positive and downward as negative we get, -45 = 1/2 x (-10) t2 (since, u = 0), so t = 3s. Now we will calculate the initial velocity of the stone such that it covers 55m in 3 seconds. So, 55 = ux3 + 1/2 (-10)(3)2
55 = 3u - 45, 3u = 100. So, u = 100/3 m/s
100/3 m/s
Let us take the velocity with which the stone is thrown is equal to 'u' m/s. Now the time 't' at which they meet is actually the time in which the ball covers a distance of (100 - 55) = 45m. SO, taking upward direction as positive and downward as negative we get, -45 = 1/2 x (-10) t2 (since, u = 0), so t = 3s. Now we will calculate the initial velocity of the stone such that it covers 55m in 3 seconds. So, 55 = ux3 + 1/2 (-10)(3)2
55 = 3u - 45, 3u = 100. So, u = 100/3 m/s
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