Answer:
a. 4v/3 b. The collision is elastic.
Step-by-step explanation:
(a) the final speed of the car in terms of the initial speed of the truck
From the law of conservation of momentum, the initial and final momentum of the system is the same.
So, Mv + mV = Mv' + mV' where M = mass of truck, v = initial velocity of truck, v' = final velocity of truck = v/3, m = mass of car = M/2, V = initial velocity of car = 0 (since it was initially at rest) and V' = final velocity of car.
So, substituting the values of the variables into the equation, we have
Mv + mV = Mv' + mV'
Mv + M/2 × 0 = Mv/3 + (M/2)V'
Mv + 0 = Mv/3 + (M/2)V'
Mv - Mv/3 = (M/2)V'
2Mv/3 = (M/2)v'
v' = 2Mv/3 ÷ M/2
v' = 4v/3
(b) if the collision is elastic or inelastic
The collision is elastic if the initial kinetic energy equals the final kinetic energy.
So, initial kinetic energy K = initial kinetic energy of truck + initial kinetic energy of car = 1/2Mv² + 0 = 1/2Mv²
Final kinetic energy K' = final kinetic energy of truck + final kinetic energy of car = 1/2Mv'² + 1/2mV'²
= 1/2M(v/3)² + 1/2(M/2)(4v/3)²
= Mv²/(2 × 3²)(1 + 4²/2)
= (Mv²/18)(1 + 16/2)
= (Mv²/18)(1 + 8)
= 9Mv²/18
= Mv²/2
Since K = 1/2Mv² = K' = 1/2Mv², <u>the collision is elastic</u>.
