Question: A 1070 kg car and 3420 kg truck undergo a perfectly inelastic collisio

Question

Question:

A 1070 kg car and 3420 kg truck undergo a perfectly inelastic collision. Before the collision, the car was traveling southward at 1.45 m/s and the truck was westward at 9.20 m/s. Find the velocity of the wreckage immediately after the collision.

You can take this into account by one of these methods:
  1) Use conservation of momentum and use i-j unit vector notation throughout
  2) Write the equations for conservation of momentum in the x direction, and in the y-direction, separately, and solve the two equations simultaneously.

If you use method 1, be sure that you state the directions being taken as positive.  No need to do that for method 2, since the unit vectors are defined as positive in the north and east directions.

Explanation / Answer

First off, what is a perfectly inelastic collision? Its a collision where once the objects collide, there is no rebound. They essentially become one object.

By calculating the momentum of each before the collision, we can obtain a total momentum. Lets make north our positive Y for easy calculation

First, the car.

momentum in x direction or Px

Px=0 (easy)

Py=(1070kg*1.45)=1551.5kg(m/s)

now the truck

Px=(3420kg*-9.2m/s)=-31464kg(m/s) negative because west is our negative x direction

Py=0 easy

now that they are collided and considered one mass, because of conservation of momentum, Pi=Pf, so we get:

-31464i+1551.5j=4490kg*v

v=(-7.00i+0.3255j)m/s

so for whatever notation you need to use, the final velocity is

Vx = -7 m/s

Vy = 0.3255 m/s

any questions just ask :)

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