Question

A car with a mass of 1380 Kg is traveling at 23 m/s to the north. A truck with a mass of 1625 Kg is traveling at 26 m/s to the south. Imagine that both of these vehicles crash into each other head-on and get stuck together. What will their velocity be immediately after the collision

Answer 1

Answer: -3.49 m/s (to the south)

Step-by-step explanation:

This problem can be solved by the Conservation of Momentum principle which establishes the initial momentum
`p_(i)` must be equal to the final momentum
`p_(f)`, and taking into account this is aninelastic collision:

Before the collision:

`p_(i)=mV_(o)+MU_(o)` (1)

After the collision:

`p_(f)=(m+M)V_(f)` (2)

Where:

`m=1380 kg` is the mass of the car

`V_(o)=23 m/s` is the velocity of the car, directed to the north

`M=1625 kg` is the mass of the truck

`U_(o)=-26 m/s` is the velocity of the truck, directed to the south

`V_(f)` is the final velocity of both the car and the truck

`p_(i)=p_(f)` (3)

`mV_(o)+MU_(o)=(m+M)V_(f)` (4)

Isolating
`V_(f)`:

`V_(f)=(mV_(o)+MU_(o))/(m+M)` (5)

`V_(f)=((1380 kg)(23 m/s)+(1625 kg)(-26 m/s))/(1380 kg+1625 kg)` (6)

Finally:

`V_(f)=-3.49 m/s` The negative sign indicates the direction of the velocity is to the south