Two particles A and B are projected from ground towards each other with speeds `10 m//s` and `5(sqrt2) m//s` at the angle `30^@ and 45^@` with horizontal from two points separated by a distance of 15 m.
will they collide or not ?

Explanation

For collision to take place, relative velocity of A with respect of B should be along Ab or their
vertical components should be same.
Vertical components of A
`v_1 = 10 sin 30^@ = 5 m//s`
and vertical component of B
`v_2 = 5(sqrt2) cos 45^@ = 5 m//s`
Since, `v_1 = v_2`, so they may collide
Now the second condition is ,
`R_1+R_2 ge d (d=15 cm)`
`:. R_1 = ((10)^2sin60^@)/10 = 8.66 m`
`R_2 = ((5sqrt(2))^2sin90^@)/10 = 5m`
Since, `R_1+R_2 ltd`, so they will not collide.