Question

# A 0.10 kg object with a speed of 2.0 m/s in the +x direction makes a...

A 0.10 kg object with a speed of 2.0 m/s in the +x direction makes a head-on elastic collision with a 0.15 kg object moving in the -x direction with a speed of 3.0 m/s. What is the final velocity of the 0.10 kg object after the collision?

a. – 4.0 m/s

b. + 1.0 m/s

c. - 1.0 m/s

d. + 4.0 m/s

In a perfectly elastic collision, Using momentum conservation

Pi = Pf

m1V1i + m2V2i = m1V1f + m2*V2f

given that m1 = mass of object 1 = 0.10 kg

m2 = mass of object 2 = 0.15 kg

V1i = initial speed of object 1 = +2.0 m/s

V2i = initial speed of object 2 = -3.0 m/s

0.10*2.0 + 0.15*(-3.0) = 0.10*V1f + 0.15*V2f

-0.25 = 0.10*V1f + 0.15*V2f

2*V1f + 3*V2f = -5

Now In elastic collisions, since coefficient of restitution is 1, So

V1f - V2f = V2i - V1i

V1f - V2f = -3.0 - 2.0

V1f - V2f = -5.0

3*V1f - 3*V2f = -15.0

Now Solving both equation

5*V1f = -20.0

V1f = velocity of object 1 after collision = -4 m/s (in left direction)

V2f = velocity of object 2 after collision = +1.0 m/s (in right direction)

Speed of 0.10 mass just after collision = -4.0 m/sec

Therefore correct option is a.