Question

As shown in figure, a body is projected with velocity U1 from the piont A. At the same time another body is projected vertically upwards with the velocity U2 from the point B. What should be the value of U1/U2 for both the bodies to collide?

Answer 1

Let both bodies collide after t sec.
displacement in vertical direction by 1st particle = displacement in y direction by 2nd particle

1st particle is projected with speed $u_1$ at an angle 60° with horizontal.
after time t sec vertical displacement, S
S = $u_1sin60^{\circ}t-\frac{1}{2}gt^2$

displacement of 2nd particle after time t sec.
S = $u_2t-\frac{1}{2}gt^2$

$u_1sin60^{\circ}t-\frac{1}{2}gt^2=u_2t-\frac{1}{2}gt^2$

$u_1sin60^{\circ}t=u_2t$

$\frac{u_1}{u_2}=\frac{1}{sin60^{\circ}}$

$\frac{u_1}{u_2}=\frac{2}{\sqrt{3}}$