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 1750 kg and was approaching at 6.00 m/s due south. The second car has a mass of 750 kg and was approaching at 25.0 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.)

Explanation / Answer

(a)

Use conservation of momentum

In the West direction

1750(0) + 750(25.0) = (1750 + 750)vx

vx = 7.5m/s

In the South direction

1750(6.00) + 750(0) = (1750 + 750)vy

vy = 4.2m/s

v = (7.5² + 4.2²)

v = 8.6 m/s

tan = 4.2 / 7.5

= 29.25º South of West

(b)

Kinetic energy lost

½(1750)6.0² + ½(750)25² - ½(1750+750)8.6² = 173,425J

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