Two vehicles approach a right angle intersection and then co

Two vehicles approach a right angle intersection and then collide. After the collision, they become entangled. If their mass ratios were 1:3 and their respective speed as Approached were both 14 m/s. find the magnitude and direction of the final velocity of the wreck.

Solution

suppose mass of ligher is m then mass of other vehicle is 3m.

If initial velocity of one is 14i m/s then velocity of other is 14j m/s .

using momentum conservation,

initial momentum = final momntum

m x 14i + 3m x 14j = ( m + 3m)vf

vf = 3.5i + 10.5 j m/s

magnituide   = sqrt(3.5^2 + 10.5^2) = 11.07 m/s

angle with lighter vehicle\' s initial motion directoion = tan^-1(10.5/3.5) = 71.57 deg