Two particles having position vectors `vecr_1=(3hati+5hatj)m` and `r_2 =(-5hati + 3hatj) m` are moving with velocities `V_1 = (4hati +3hatj)m/s` and `V_2 = (-ahati + 4hatj) m/s` . If they collide after `2` s, the value of `a` is

Options

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

Answer

d

Explanation

Time taken in collision, t=r/v
resulting position vector, `r=vecr_(1)-vecr_(2)`
=`8hati+8hatj`
Resulting velocity, `V=vecV_(2)-vecV_(1)=(a-4)hati+4hatj`
At` t=2s,
Equation (1) `2=`(8hati+8hatj)/(a-4)hati+4hatj) `
`(a-4)hati+4hatj=4hati+4hatj`
`ahati-4hati+4hatj=4hati+4hatj`
`a(hati)=8hati)`
a=8`