# Solving Collision Question: Find Initial Velocities of Cars

• ~angel~
In summary, the car traveling east has a greater mass and therefore has more momentum, which causes the car to travel at a higher velocity after the collision.
~angel~
Sorry about this but I don't have a picture, but it is of two cars, one traveling north, the other traveling east, and they collide completely inelastically. The mass of the car traveling east is 950kg, and the mass of the car traveling north is 1900kg. Their final combined velocity is 16m/s, at an angle of 24 degrees east of north. What is each cars' initial velocity?

I worked out an equation for the final momentum, using vectors:

(950v_1)^2 + (1900v_2)^2 = 45600^2

but I don't know how to solve it.

Thank you.

~angel~,
You might like to post ur complete working.
I have not done any calculations yet, but one look at your equation suggests to me that something is wrong.

If u post ur working, it would be easier to iron out your problems.

-- AI
P.S -> I believe ur working is wrong because i think u should have got two equations which u need to solve simultaneously. Ofcourse, this is my knee jerk reaction, so its better to see ur working before making any more comments.

I can't get any further than that. I'm completely lost and I don't know what I've done wrong.

This is not an assignment from mastering physics or anything, it's just a question from University Physics (Y&F) that I don't exactly understand. I thought that you're menat to use vectors to solve the equation. Sorry about this.

Your problem is that you have only one equation for 2 unknown speeds which, of course, cannot be solved! The reason you have only one equation is that you are only looking at the magnitude of the momentum when, in fact, momentum is a vector quantity. You need to look at the individual components.

Car 1 is 950 kg and moving east so we can write its velocity vector (v1,0) and its momentum (950v1,0).
Car 2 is 1900 kg and is moving north so we can write its velocity vector (0,v2) and its momentum (0,1900v2)

The total momentum, before the collision, is (950v1,1900v2).

After the collision, since it is "completely inelastic", the two cars move as a single
1900+ 950= 2850 kg mass at "16m/s, at an angle of 24 degrees east of north". Drawing a right triangle representing that, we see that we can write the velocity vector as (16 sin(24), 16 cos(24)) and so the momentum vector is (2850*16 sin(24), 2850*16 cos(24))= (45600 sin(24), 45600 cos(24)).

"Conservation of momentum" requires (950v1,1900v2)= (45600 sin(24), 45600 cos(24)) or v1= 45600 sin(24) and 1900v2= 45600 cos(24).

Those should be easy to solve.

I understood that I couldn't solve the equation I found =P

## 1. What is a collision and why is it important to solve?

A collision is a situation where two or more objects come into contact with each other and exert forces on one another. It is important to solve collisions because they can lead to damage, injuries, and even death in certain situations. By understanding the initial velocities of cars involved in a collision, we can better understand the forces at play and potentially prevent future accidents.

## 2. How do you determine the initial velocities of cars in a collision?

To determine the initial velocities of cars in a collision, we need to use the principles of conservation of momentum and conservation of energy. First, we measure the mass and final velocities of the cars after the collision. Then, using the formulas for momentum and kinetic energy, we can solve for the initial velocities of the cars before the collision.

## 3. What factors can affect the initial velocities of cars in a collision?

The initial velocities of cars in a collision can be affected by factors such as the mass of the cars, the angle of impact, the speed of the cars, and the type of material the cars are made of. Other factors, such as air resistance and friction, can also play a role in the final velocities of the cars.

## 4. Can the initial velocities of cars in a collision be calculated accurately?

While it is possible to calculate the initial velocities of cars in a collision, it may not always be accurate. This is because there are many variables and factors that can affect the outcome of a collision. Additionally, human error in measuring and recording data can also impact the accuracy of the calculations.

## 5. How can the initial velocities of cars in a collision be used in accident reconstruction?

The initial velocities of cars in a collision can be used in accident reconstruction to understand how the collision occurred and potentially determine who is at fault. By analyzing the initial velocities, along with other factors such as skid marks and damage to the vehicles, investigators can piece together the sequence of events leading up to the collision and make a determination on the cause of the accident.

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