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
Add both of them
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.
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