Question

A 50 kg teenager just got his license and is driving his brand new Escalade (mass 1100 kg) at 30 m/s. As he is texting and driving, he crashes into a stopped minivan, which has a mass of 980 kg. Since he is not wearing a seatbelt, he flies out of the window after the crash. If the Escalade and Minivan move together with a speed of 13 m/s after the perfectly elastic crash, with what velocity is the teenage (former) driver now flying through the air?

Answer 1

let u1 & u2 be the velocity of the car and mnivan before
collision.let v1 & v2 be the velocities after collision.

initial momentum of the system before collision is

Pi = m1*u1 + m2*u2

final momentum of the system after collision is

Pf = m1*v1+m2*v2

elastic collisions   the total momentum is conserved .

the momentum before collision = momentum after collision

according to conservation of linear momentum

m1*u1 + m2*u2 = m1*v1+m2*v2

m1*(u1-v1) = m2*(v2-u2)........(1)

initial KE of the system KEi = 0.5*m1*u1^2 + 0.5*m2*u2^2

final KE of the system KEf = 0.5*m1*v1^2 + 0.5*m2*v2^2

according to conservation of energy

0.5*m1*u1^2 + 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2

m1*(u1^2 - v1^2) = m2*(v2^2-u2^2).....(2)

from 1 &2

u1 + v1 = u2+v2

u1 - u2 = v2 - v1

v2 = u1 - u2 + v1........(3)

3 in 1

m1*(u1-v1) = m2*(u1 - u2 + v1 - u2)

v1 = u1*(m1-m2)/(m1+m2) + 2*m2*u2/(m1+m2)

v2 = u2*(m2-m1)/(m1+m2) + 2*m1*u1/(m1+m2)

m1 = 1150 kg                 m2 = 980 kf

u1 = 30...........u2 = 0

v1 = ?...........v2 = ?

v1 = ((1150-980)*30)/(1150+980) = 2.39 m/s <-----------answer

v2 = (2*1150*30)/(1150+980) = 32.39 m/s   <-----------answer