Question

A ball is dropped from the top of the building 100m
high. Simultaneously, another ball is thrown upwards
from the bottom of the building with such a velocity
that a balls collide exactly midway. What is the speed in
m/s with which the second ball is thrown?
(Take g = 10 m/s2)
(a) 31.6 (b) 27.8 (C) 22.4 (d) 19.6
​

Answer 1

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For ball 1 time taken by it to reach midway =t

And gravity acts in direction of motion

$From\\S=ut+\frac{1}{2}at^{2} \\50m=0(t)+\frac{1}{2}\times 10 \times t^{2}\\ 50=5t^{2}\\t=\sqrt{10}=3.15s$

for ball 2 gravity acts in opposite direction of motion

hence

$S=ut+\frac{1}{2}at^{2}\\ 50=u(t)-\frac{1}{2}\times 10\times t^{2}\\ 50=3.15u-5\times (3.15)^{2}\\50=3.15u-50\\3.15u=100\\u=31.6m/s$