Two objects, A and B, of equal mass, collide and deflect off each other. The ini

Question

Two objects, A and B, of equal mass, collide and deflect off each other. The initial velocities of
objects A and B are <15, 30> m/s and <-10, 5> m/s, respectively. Afterward the velocity of
object A is <-5, 20> m/s. (a) What is the final velocity of object B? (b) What is the change in
the kinetic energy of the system (including sign)? See problem 4 for the definition of kinetic
energy and note that the square of a vector is a positive scalar whose magnitude is equal to the
square of the magnitude of the vector.

Explanation / Answer

=> m1u1 + m2u2 = m1v1 + m2v2

so m ( u1 + u2) = m (v1 + v2)

=> <15, 30> + <-10, 5> = <-5, 20> + <v2x , v2y>

so < 5 , 35 > = <-5 +v2x , 20 + v2y>

=> v2x = 10 , v2y = 15

hence v2 = < 10 , 15 > m/s

____________________________________________

b) KE1 = 1/2 m u1^2 + 1/2 m u2^2 = 1/2 m (  |<15, 30>|^2 + |<-10, 5|^2>

=> KE1 = 1/2 m ( 1250) = 625 m J

and KE2 = 1/2 m v1^2 + 1/2 m v2^2  = 1/2 m (  |<-5, 20>|^2 + |<10, 15|^2>

=> KE2 = 375 m J

so

delta KE = KE2 - KE1 = 375 m - 625 m = - 250m Joules

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