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 1250 kg and was approaching at 7.00 m/s due south. The second car has a mass of 700 kg and was approaching at 23.0 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)

Use conservation of momentum

In the West direction

1250(0) + 700(23.0) = (1250 + 700)vx

vx = 8.256 m/s

In the South direction

1250(7.00) + 700(0) = (1250 + 700)vy

vy = 4.487 m/s

v = ?(8.256² + 4.487²)

v = 9.4 m/s

tan? = 4.487 / 8.256

? = 28.52º South of West

(b)

Kinetic energy lost

½(1250)7.0² + ½(700)23² - ½(1950)9.4² = 129,624 J

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