Calculating Post-Collision Speed and Initial Speed of Two Cars at Intersection

[physicsjessic]

Homework Statement

Two cars collide at an intersection. car A with a mass of 2000 kg is going from west to east while car B of mass 1500 kg is going from north to south at 15 m/s. As a result of collision the two cas move together as one after. The cars now move at an angle 65 degrees south of east from point of impact.
How fast are the cars moving after collision?
How fast was car A going just before the collision?

Homework Equations

conservation of momemtum

The Attempt at a Solution

P intail= P final

 

[tiny-tim]

Hi physicsjessic!

Homework Equations

conservation of momemtum

Yes, that's the right technique …

what do you get? ​

 

[nlightner]

m1v1 + m2v2 = (m1+m2)vfinal
(2000 kg)(v1) + (1500 kg)(15 m/s) = (2000 kg + 1500 kg)(vf)
2000v1 + 22500 = 3500vf

To find the post-collision speed, we can use the conservation of momentum equation, which states that the initial momentum of the system is equal to the final momentum of the system. In this case, the initial momentum is the sum of the individual momentums of car A and car B, while the final momentum is the momentum of the combined cars after the collision.

We can rearrange the equation to solve for the final velocity (vf):

vf = (2000v1 + 22500) / 3500

To find the initial speed of car A, we can use the same equation but substitute the final velocity with the velocity at the point of impact, which is the velocity of the combined cars moving at an angle of 65 degrees south of east. This can be found using trigonometry:

vf = √((v1)^2 + (15 m/s)^2 + 2(v1)(15 m/s)cos(65 degrees))

By solving for v1, we can find the initial speed of car A just before the collision.