Question

A 2100 kg truck is driving south through an intersection at 40 mph when it crashes into a 1200 kg car that was driving east through the intersection at 55 mph. The two vehicle stick together in a sad, scary, twisted mess. What is the velocity (both magnitude and direction) of the wreckage immediately after the collision, before the vehicles have had any time to slow due to friction?

Answer 1

Mass of the truck M = 2100 kg

Initial velocity of the truck U = 40 (-j) mph

Mass of car m = 1200 kg

Initial velocity of the car u = 55 i mph

Where i and j are the unit vectors along east and north directions respectively.

From law of conservation of linear momentum ,

    mu + MU = (M+m) v

(1200 x 55 i ) +(2100 x -40 j) = (2100+1200) v

66000 i -84000 j = 3200 v

From this velocity of the both after collision v = (66000 i -84000 j )/3200

                                                                  = 20.625 i-26.25 j

Magnitude of v = [20.625 ² + (-26.25) ²]

                      = 33.38 mph

Let v makes an angle with east direction then tan = -26.25 / 20.625

                                                                                = -1.27

                                                                             = -51.84 ^o

i.e., both the vehicles are moved 51.84 ^o south of east

If the you give coefficient of friction between tires and road then you find time t

accleration a = -g

Final velocity V = 0

from the relation V = v + at   you find t value