Question

Two particles projected vertically upward from points (0,0) and (1,0) with uniform velocity 10 m/s and v m/s, respectively, as shown in the figure. It is found that they collide after time t in space. Find v and t.

Answer 1

Considering motion in horizontal direction,time taken to collide,

$t=\frac{1}{\frac{10\sqrt{3}}{2}-\frac{v}{\sqrt{2}}}$

$t=\frac{2\sqrt{2}}{10\sqrt{6}-2v}$...(1)

In vertical direction, $10\times \frac{1}{2}t-\frac{1}{2}g{t}^2=\frac{v}{\sqrt{2}}\times t-\frac{1}{2}g{t}^2$

$5=\frac{v}{\sqrt{2}}$

$v=5\sqrt{2}$

$t=\frac{2\sqrt{2}}{5\sqrt{6}-10\sqrt{2}}=1.49$ seconds