A 70 kg mother skates on frictionless ice at 2 m/s to the right, towards her 30

Question

A 70 kg mother skates on frictionless ice at 2 m/s to the right, towards her 30 kg daughter who is skating left at 3 m/s. The mother and daughter meet ("collide") and skate off together a) find the speed and direction which the mother-daughter pair skate off after they meet b) what principle or law of physics did you use to solve part a, and how did you know that was the correct principle to apply? c) determine whether or not the collision between mother and daughter was elastic (show your calculations-do NOT assume the answer) d) Discuss whether or not your answer to part a and c are reasonable. Provide specific reasons why you think your answers are or are not reasonable. If you did not answer one of the parts, then, you may tell what type of answer one would expect to obtain. YOU MUST SHOW ALL WORK, STARTING WITH THE BASIC EQUATIONS, RECEIVE CREDIT

Explanation / Answer

here,

initial speed of mother , u1 = 2 m/s

mass 1 , m1 = 70 kg

initial speed of mother , u2 = - 3 m/s

mass 2 , m2 = 30 kg

a)

let their final speed be v

using conservation of energy

m1 * u1 + m2 * u2 = (m1 + m2) * v

70 * 2 - 30 * 3 = ( 70 + 30) * v

v = 0.5 m/s

the final velocity is 0.5 m/s towards right

b)

we had used principle of conservation of linear momentum

as the motion of the bodies is linear and there is no net external force acting on them

c)

initial kinetic energy , KEi = 0.5 * ( m1 * u1^2 + m2 * u2^2)

KEi = 0.5 * ( 70 * 2^2 + 30 * 3^3)

KEi = 275 J

final kinetic energy , KEf = 0.5 * ( (m1 + m2) * v^2)

KEf = 0.5 * 100 * 0.5^2

KEf = 12.5 J

as the initial kinetic energy is not equal to final

the energy is not conserved

the collison is not elastic

d)

Yes , the answer to part A and C are resonable

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