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Kinematics of Two Balls

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Two balls are thrown upward from the edge of a cliff in example 6 (see attachment). The first is thrown with a speed of 48 ft/s and the other is thrown a second later with a speed of 24 ft/sec. Do the balls ever pass each other?

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Please refer to the attachment.

Let us consider upwards direction as +ve and downwards as -ve.

Let the first ball be thrown upwards at time instant t = 0. The ball is subjected to acceleration due to gravity of -32ft/s2 (-ve sign because acceleration due to gravity always acts downwards). By definition, acceleration is the rate of change of velocity. Hence, we can write the following equation :

a = dv/dt = -32 or dv = -32dt

Integrating both sides we get : v = -32∫dt + C = -32t + C where C is the constant ...

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