Question

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
° (counterclockwise from west is positive)

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

Answer 1

(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