Collision of Two Cars: Calculating Velocity

[VelvetRebel]

Homework Statement

A 850 kg car is traveling west at 25.0 m/s when it collides with a 1050 kg car that was initially traveling north at 10.5 m/s. The cars lock together, and eventually skid to a stop.
What is the velocity of the cars immediately after the collision?

Homework Equations

p_i=p_ix i + p_iy j + p_iz k

The Attempt at a Solution

I got an answer but I'm not sure if it is correct. I just need someone to verify if what I did is correct.
Here's what I did:
I found p_i using the equation above and then took the magnitude of that to find p_f as shown below:

(-(850 kg)(25.0 m/s) i)² + ((1050 kg)(10.5 m/s) j)²=p_f²

I then took the p_f value and set that equal to the total mass times the velocity:

2.39 x 10⁴ kg*m/s=(850 kg + 1050 kg)v

I then solved for v to get the following:

v=12.6 m/s

 

[rl.bhat]

Your answer is correct.

 

[kerimek]

To verify this answer, we can use the conservation of momentum principle, which states that the total momentum before a collision is equal to the total momentum after the collision. In this case, we can calculate the total initial momentum as:

p_initial = (850 kg)(25.0 m/s) + (1050 kg)(10.5 m/s) = 21,250 kg*m/s + 11,025 kg*m/s = 32,275 kg*m/s

And the total final momentum as:

p_final = (850 kg + 1050 kg)(v) = 1,900 kg*v

Setting these two values equal to each other and solving for v, we get:

32,275 kg*m/s = 1,900 kg*v

v = 32,275 kg*m/s / 1,900 kg = 17.0 m/s

This confirms that the velocity of the cars immediately after the collision is 17.0 m/s, which is different from the value you calculated. This could be due to a mistake in the calculations or assumptions made. It's always a good idea to double check your work and make sure all units are consistent in your equations. Additionally, it's important to consider any external factors that could affect the outcome of the collision, such as friction or air resistance. Overall, it's important to approach scientific problems with caution and verify your results to ensure accuracy.