Two problems...?

Question

(A)Two students on roller skates stand face to face then push each other away. One student has a mass of 96kg and the other student has 60kg.

Find the ratio of the magnitude of the first student's velocity to the magnitude of the second student's velocity.

(B) A 2080 kg car moving east at 10.1 m/s collides with a 3270 kg car moving 3.99m/s east. The cars stick together and move east as a unit after the collision at a velocity of 6.27 m/s.

What is the decrease in kinetic energy during the collision in units of m/s?

Answer 1

A) Momentum problem
Initial Momentum = Final Momentum

Since there is no Initial momentum

m1v1f = m2v2f

v1f = m2/m1*v2f ==> v1f = 96/60 *v2f

96/60 is the ratio, or 1.6/1

B)
Total Energy intially = 1/2*m1*v1^2 + 1/2*m2*v2^2
Total Energy final = 1/2 (m1+m2)*vf^2

Ei - Ef = answer

Answer 2

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Answer 3

1. m1V1=m2V2
V2/V1=m1/m2
V2/V1= 96/60=1.6
V2=1.6V1

2. In general Ke1 + Ke2 = Ke + dKe
dKe = Ke1 + Ke2 - Ke
dKe= 0.5(m1) V1^2 +- 0.5 m2 V2^2 - 0.5 (m1+m2) V^2
dKe= 0.5[ 2080 x (10.1)^2 + 3270 x (3.99)^2 - ( 2080 + 3270) x (6.27)^2 ]
dKe= 53,920 J