# How do I solve this problem? Pls help!?

Two vehicles approach an intersection at right angles. Sadly, they collide. After the collision, they become entangled. If their mass ratios were 1:4 and they both approached the intersection with a speed of 13 m/s, find the magnitude of the final velocity of the wreck.

### 1 Answer

- 7 years agoFavorite Answer
You're probably in Meldrum's Physics 124 class at the University of Alberta judging by the word for word copy & paste of the assignment question. I strongly caution you against asking so blatantly in the future as this could be perceived as cheating. However, since the assignment just expired, I don't see any harm in answering your question.

This is a conservation of momentum question. You need to:

1) Find the momentum before the impact. Remember that these cars are moving in different planes of direction and you need the net momentum in the situation. Think vector addition.

2) Recall that momentum is conserved, and this is a hit 'n' stick collision.

3) Find the formula for the momentum after the collision, and isolate the variable "vf" for the final velocity of the wreck.

So,

1) Find the initial momentum. Pi = vector sum of (m1v1 E & m2v2 N). Use Pythagorean Triangle to find the vector sum of these two vehicles. Remember that one car has 4x the mass of the other. Since this is arbitrary and gets divided out in the end, we can simple use coefficients of 1 and 4 to make our lives simple.

You will find that the total initial momentum is equal to sqrt((4*13)^2 + (1*13)^2) = sqrt(52^2 + 13^2) = 53.600... kg*m/s, or 53.600... N*s.

2) The formula for pf (the final momentum) is equal to (m1 + m2)*vf. Isolate the final velocity, vf, to get your answer.

3) Since momentum is conserved, then pi = pf. This means that 53.600... kg*m/s = (m1 + m2)*vf. Vf = [ 53.600... kg*m/s ] / (m1 + m2) = 53.600/(4 +1 ) = 53.600/5 = 10.72007463 m/s

Since we ignore sig digs in the assignment questions, we'll just keep as many digits as possible :)

Hope this helped!

Source(s): Lecture material and course notes.