Two particles having position vectors `vec(r )_(1) = ( 3 hat(i) + 5 hat(j)) meters` and `vec( r)_(2) = (- 5 hat(i) - 3 hat(j)) metres` are moving with velocities `vec(v)_(1) = ( 4 hat(i) + 3 hat(j)) m//s` and `vec(v)_(2) = (alpha hat(i) + 7 hat(j)) m//s`. If they collide after `2 s`, the value of `alpha` is

Options

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

Answer

D

Explanation

` vecr_1 =( 3 hat + 5 hat j) m, vecr= (-5 hat i-3 hat j)m`
:. ` Delta vec r= vec r_2`
`= (3 hat I +5 hat j) - (-5 hat i-3 hat j) = (8 hat I +8 hat j) m`
` vec v_1 = (4 hat + 3hat j) m//s , vec v_2 = (ahat i+7 hat j) m//s`
:. ` As ` Delta vec v= (Delta vec t)/(Delta t),
` so ` (a-4 ) hat i + 4 hat j= ( 8 hat i + 8 hat j) //2`
On solving , we get, ` a=8`.