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 1050 kg and was approaching at 5.00 m/s due south. The second car has a mass of 750 kg and was approaching at 19.0 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

Let speed be v, and angle with west be theta.

By momentum conservation in x direction,

750*19 = (750+1050) v cos theta

By momentum conservation in y,

1050*5 = (750+1050) v sin theta

dividing it by first equation,

(1050*5)/(750*19) = tan theta

theta = arctan ((1050*5)/(750*19)) = 20.22 degree

magnitude of v = 1050*5/( 1800 sin 20.22 degree )

= 8.44 m/s

direction = 20.22 degree

b) kinetic energy lost = Initial KE - Final KE = 0.5*750*19^2 + 0.5*1050*5^2 - 0.5*(1050+750)*8.44^2

= 84390 J answer

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