A 1.36 10 3 -kg car traveling initially with a speed of 20.0 m/s in an easterly

Question

A 1.36  103-kg car traveling initially with a speed of 20.0 m/s in an easterly direction crashes into the rear end of a 9.00  103-kg truck moving in the same direction at 15.0 m/s. The velocity of the car right after the collision is 13.0 m/s to the east. What is the velocity of the truck right after the collision? (Assume east is the positive direction. Indicate the direction with the sign of your answer.)
1 m/s

    How much mechanical energy is lost in the collision? (Use the exact value you entered the first part to make this calculation.)
2 J

Explanation / Answer

using conservation of linear momentum,

m1u1 + m2u2 = m1v1 + m2v2

=> 1360*20 + 9000*15 = 1360*13+ 9000*v2

so v2 = 16.0577777778m/s in easterly dirn.

energy before collision = 1/2*m1*u1^2 + 1/2*m2*u2^2

=> E1 = 0.5*1360*20^2 + 0.5*9000*15^2 =1284500 J

energy after collision = 1/2*m1*v1^2 + 1/2*m2*v2^2

=> E2 = 0.5*1360*13^2 + 0.5*9000*16.0577^2 =1275243.78181J

so energy lost = E1 - E2 = 9256.218195 J

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