From the top of a tower 100m high a ball is dropped and at the same instant another ball is projected vertically upwards from the ground so that it just reaches the top of the tower.At what height do the two balls pass one another?

Let two balls meet at some point which is at distance x from the ground.
Now both the ball will reach to the point in same time t.

for the first ball100 -x = ut +1/2at2u = 0 , a = g100 - x = 4.9t2 -----(1)

for the second ball final speed = 0initial speed is u'distnace travelled = 100 mv2-u'2 = 2asa = -gu' = 44.27 m/stherefore using second equation of motionx = 44.27t - 4.9t2 ---(2)

Solve the equation (1) and (2) and you will get
t = 2.26 s
x = 74.98 m

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