Question

Car A with a mass of 1000kg is travelling east at 25m/s when it collides with car B, 2000kg, travelling north at 15m/s. After the collision, the two cars stick together and have the same velocity. Assume that they slide without friction after collision.

(a) What is the final velocity of the combined mass of cars (magnitude and direction)?

(b) How much kinetic energy was lost in this process and where did it go?

Answer 1

a. M1V1 + M2V2 = M1V + M2V.
1000*25 + 2000*15i = 1000V + 2000V,
25,000 + 30,000i = 3000V,
Divide by 1,000:
25 + 30i = 3V, V = 13m/s[50.2o] N. of E.

Answer 2

b. KE1 = 0.5M1*V1^2 + 0.5M2*V2^2,
KE1 = 500*25^2 + (1000*15i^2),
KE1 = 312,500 + 225,000 = 537,500 J. = KE before collision.

KE2 = 0.5M1*V + 0.5M2*V.
KE2 = 500*13^2 + 1000*13^2 = 253,500 J. = KE after collision.

KE1-KE2 = KE lost after collision.