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A ball is dropped from a top of a tower of 100 m height. Simultaneously another ball was thrown upward from bottom of the tower with a speed

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Secondary SchoolPhysics 5 points

A ball is dropped from the top of a tower 100m high. Simultaneously another ball is thrown upward with a speed of 50m/s. after what time do they cross each other

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⇒ the time taken by both balls at point P has same time ' t ' seconds .

⇒ for first ball , that is in the diagram from A to P

S = ut + 1/2 at²

we know that u = 0 and a = g

⇒ ( 100 - x ) = (0)t + 1/2 gt²------------(1)

now, for the second ball from B to P in the diagram ,

S = u't + 1/2 at²

where u = 50 m/s and a = -g

therefore, x = 50(t) - 1/2gt² ------------------(2)

by adding equation (1) and (2) we will get ,

100 = 50 t

implies, t = 100 / 50

therefore t = 2 sec .

therefore the time that they cross each other is 2 seconds.