Two particles having position vectors `vec(r_1) = (3hati +5hatj) m` and `vec(r_2) =(-5hati-3hatj)` m are moving with velocities `vec(v_1) = (4hati +3hatj)ms^(-1)` and `vec(v_2) = (a hati + 7 hatj) ms^(-1).` If they collide after 2 seconds, the value of a is 

Options

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

Answer

D

Explanation

Here, `vec(r_1) = (3hati + 5hatj) m, vec(r_2) = (-5 hati - 3hatj) m`,
`vecv_1 = (4hati + 3 hatj) ms^(-1), vec(v_2) = (a hati + 7 hatj) ms^(-1)`
`:. Delta vec(r) = vec(r_1) - vec(r_2) = (3 hati + 5 hatj) - (5hati - 3hatj) = (8 hati + 8 hatj) m`
and `Delta vecv = vec(v_2) - vec(v_1) = (a - 4) hati + 4hatj`
But `Delta vec(v) = (Delta vecv)/(Delta t) :. (a - 4) hati + 4hatj = ((8 hati + 8 hatJ))/(2)`
On solving , we get `a = 8`