A 1 160.0 kg car traveling initially with a speed of 25.000 m/s in an easterly direction crashes into the back of a 9 900.0 kg truck moving in the same direction at 20.000 m/s. The velocity of the car right after the collision is 18.000 m/s to the east.

a. What is the velocity of the truck right after the collision?
b. What is the change in mechanical energy of the car's truck system in the collision?
c. Account for this change in mechanical energy.

Explanation:

a ) We shall apply law of conservation of momentum

initial momentum of car and truck

= 1160 x 25 + 9900 x 20

= 29000 + 198000

= 227000 kg m/s

let velocity of truck after collision be v

total momentum after collision

= 1160 x 18 + 9900 v

Applying conservation of momentum law

227000 = 1160 x 18 + 9900 v

20880 + 9900 v = 227000

9900 v = 206120

v = 20.82  in the same direction ie towards the east.

b ) Initial kinetic energy of car and truck

= 1/2 x 1160 x 25² + 1/2 x 9900 x 20²

= 362500 + 1980000

= 2342500 J

final kinetic energy of car and truck

= 1/2 x 1160 x 18² + 1/2 x 9900 x 20.82²

= 187920 + 2145688.38

= 2333608 .38 J

loss of energy = 8892 J

c ) Change in mechanical energy is due to  transformation of energy into heat and sound during collision .