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 1600 kg and was approaching at 8.00 m/s due south. The second car has a mass of 900 kg and was approaching at 16.0 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] By using Conservation of momentum,

In the west direction

1600*0+ 900*16 = (1600+900)Vx

Vx = (1600*0+ 900*16)/ (1600+900)

= 5.76 m/s

In the south direction

1600*8 + 900*0 = (1600+900)Vy

Vy = (1600*8 + 900*0)/(1600+900)

= 5.12 m/s

Let the final velocity of car be V,

V = sqrt(Vx^2 + Vy^2)

= sqrt(5.76^2 + 5.12^2)

= 7.7 m/s magnitude

Direction

tan theta = Vy / Vx

theta = arctan(5.12/5.76)

= 41.63 degree

b] Kinetic energy lost in the collision, K.E

= 0.5*1600*8^2 + 0.5*900*16^2 - 0.5*(1600+900)*7.7^2

= 92287.5 J answer

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