Two particles having position `vec(r_(1))=(3hat(i) + 5hat(j))` meter and `vec(r_(2))=(-5hat(i)-3hat(j))` metre are moving with velocities `vec(V_(1))=(4hat(i)+hat(j))`m/s and `vec(V_(2))=(ahat(i) + 7hat(j))` m/s. If they collide after 2 seconds, the value of `a` is :

Options

A. 2
B. 4
C. 6
D. 8

Answer

D

Explanation

Here `Deltavec(r)=vec(r_(2))-vec(r_(1))=-8hati-8hatj`
As the particles are moving in the same direction, the relative velocity is given by the difference of two velocities.
`vec(v_(R))=(a-4)hati + 4hatj`
`|vec(v_(R))|=sqrt((a-4)^(2)+(4)^(2))`
Also `|vec(v_(R))|=|Deltavec(r)|/t`
`sqrt((a-4)^(2)+16)=(8sqrt(2))/2`
`(a-4)^(2)=16` or a - 4 = 4 and a = 8