Question

# Two cars collide at an icy intersection and stick together afterward. The first car has a...

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1500 kg and was approaching at 4.00 m/s due south. The second car has a mass of 700 kg and was approaching at 18.0 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
Â° (counterclockwise from west is positive)

(b) How much kinetic energy is lost in the collision? (This energy goes into deformation of the cars.)
J

(a) in the west direction

M1*V1 = M1V1*cos theta1 + M2V2*cos theta2

Vx (1500 + 700) = 1500 (0) + 700 (18 m/s )

Vx = 12600 / 2200

Vx = 5.72 m/s

In the south direction

Vy(1500 + 700) = (1500)(4m/s) + (700)(0)

Vy = 2.72 m/s

Magnitude is

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

= sqrt((5.72)^2 + (2.72)^2)

V = 6.33 m/s

Direction is theta = tan^-1(2.72/5.72)

theta = 25.43 degrees

(b) KE_lost = 1/2M1V1^2+ 1/2M2V2^2 - 1/2 (M1+M2) (V)^2

KE = (0.5)(1500)(4)^2 + (0.5)(700)(18)^2 - (05)(1500+700

(6.33)^2

= 81324 J

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