Two cars are in a collision at the intersection of Boyd and Elm, tying up after-

Question

Two cars are in a collision at the intersection of Boyd and Elm, tying up after-class traffic. The first car, mass 1050 kg, was heading north on Elm at 8 m/s and the second car, mass 1800 kg, was heading east on Boyd at 14 m/s.

Assuming the two cars are locked together, what is the magnitude of their velocity (speed) immediately after the collision?

Give your answer in m/s to at least three significant digits. Your answer will not be graded on the number of digits, this is just to avoid rounding error.

Explanation / Answer

initial momentum in the north direction ,,, p1 = m1 v1 = 1050*8 = 8400 kg-m/s

initial momentum in the east direction ,,, p2 = m2 v2 = 1800* 14 = 25200 kg-m/s

after collision total mass is = 1800 + 1050 = 2850kg

let final velocity be 'v' in the direction somewhere north east at an angle theta to the east direction.

initial and final momentum must be same in both the directions

in east ....... p3 = 2850 * v cos

in north ......... p4 = 2850 * vsin

equating p1 = p4 and ............p3 = p2

we get ...........v cos = 2.947 ..................... and ...............vsin = 8.842

on solving these two eqns. we get

= 71.56o

and v = 9.320 m/s

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