Answer:
a) M₂ ( the object that is stationary) b) 3 times c) the velocity is to the left
Step-by-step explanation:
let the object in motion = M₁, object stationary = M₂, the initial velocity of the M₁ = U₁, since the second object is at rest U₂ = 0, final velocity of the M₁ = V₁ and final velocity for M₂ = V₂
Using conservation law of momentum:
M₁U₁ = M₁V₁ + M₂V₂ since the second body is at rest
also
V₂ = U₁ / 2 and the collision is elastic meaning
U₁ = V₂ - V₁
U₁ = U₁ / 2 - V₁
V₁ = -U₁/2
substitute V₁ into the first equation
M₁U₁ = M₁V₁ + M₂V₂
M₁U₁ = M₁ (-U₁/2) + M₂ ( U₁/2)
collect the like terms
M₁U₁ + M₁ (U₁/2) = M₂(U₁/2)
3/2(M₁ U₁) = M₂ (U₁/2)
divide both side by U₁/2
3 M₁ = M₂
b) M₂ = 3 M₁
M₂ is three times M₁
c) V₁ = -U₁/2
since V₁ is negative, the velocity will be to the left