Two bodies are thrown vertically upwards with the same initial velocities v 0 , the second τ sec. after the first. (1) With what velocity will be second body move relative to the first ? Indicate the magnitude and direction of this relative velocity. According to what law will the distance between the bodies change ? (2) Solve this problem when the initial velocity of the second body v 0 is half the initial velocity of the first.
Text Solution
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Sol. (1) v = g τ ; (2) v = –v 0 + g τ .
In the first case the velocity of the first body at any moment relative to the earth is
v 1 = v 0 – gt
The velocity of the second body relative to the earth is
v 2 = v 0 – g (t – τ )
The required velocity of the second body relative to the first will be
v = v 2 – v 1 = g τ
The velocity v is directed upwards both during the ascent and descent of both bodies. During the ascent the distance between the bodies diminishes uniformly and during the descent it increases uniformly.
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