Two cars collide at an icy intersection and stick together afterward. The first

Question

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1500 kg and was approaching at 4.00 m/s due south. The second car has a mass of 800 kg and was approaching at 22.0 m/s due west.

(a) Calculate the final velocity of the cars. (Note that since both cars have an initial velocity, you cannot use the equations for conservation of momentum along the x-axis and y-axis; instead, you must look for other simplifying aspects..)
Magnitude
m/s
Direction
° (counterclockwise from west is positive)

(b) How much kinetic energy is lost in the collision? (This energy goes into deformation of the cars.)
J

Explanation / Answer

a)In the West direction

1500(0) + 800(22.0) = (1500 + 800)vx
vx = 7.652m/s

In the South direction

1500(4.00) + 800(0) = (1500 + 800)vy
vy = 2.61 m/s

v = (7.652² + 2.61²)
v = 8.08 m/s

tan = 2.61 / 7.652
= 33.1º South of West

b)

kinetic energy loss

0.5*1500*4*4+0.5*800*22*22-0.5*(1500+800)*8.08*8.08

130520.64

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