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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

User Firxworx
by
7.9k points

1 Answer

4 votes

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

User Slhddn
by
8.5k points
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