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 1100 kg and was approaching at 4.00 m/s due south. The second car has a mass of 750 kg and was approaching at 24.0 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

Use conservation of momentum

In the West direction

1100(0) + 750(24.0) = (1100 + 750)vx
vx = 9.73 m/s

In the South direction

1100(4.00) + 750(0) = (1100 + 750)vy
vy = 2.38 m/s

v = (9.73² + 2.38²)
v = 10.02 m/s

tan = 2.38/9.73
= 13.7º South of West


Kinetic energy lost

½(1100)4.0² + ½(750)24² - ½(1850)*10.02² = 131929.63 =>131.93 kJ

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