A car with a mass M traveling to the East at speed v collides head-on with a truck of mass 2M, traveling to the west at speed v. If they stick and move together upon colliding, what is the initial velocity of the wreckage after the collision?
If east is + and west is -, then
Mv - 2Mv = (M-2M)v = -Mv = (M+2M) * -v/3
so, it will move west with speed v/3
To determine the initial velocity of the wreckage after the collision, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v):
p = mv
Before the collision, the car's momentum (p₁) is calculated as:
p₁ = M * v (since the car has mass M and is traveling east)
The truck's momentum (p₂) is calculated as:
p₂ = (2M) * (-v) (since the truck has mass 2M and is traveling west, its velocity is considered negative)
Since they stick together and move together upon colliding, the total momentum after the collision (p_final) would be the sum of their individual momenta before the collision:
p_final = p₁ + p₂
= M * v + (2M) * (-v)
= Mv - 2Mv
= -Mv
Therefore, the initial velocity of the wreckage after the collision is -Mv (westward direction).