- #1

M Malone

- 1

- 0

## Homework Statement

"Before the collision, vehicle #1 was traveling east and vehicle #2 was traveling north.

- The driver of vehicle #1 states he was traveling 35 mph as he approached the intersection. He continues to state that vehicle #2 ran the stop sign, pulling out in front of him and causing him to crash.
- The driver of vehicle #2 states that he stopped at the stop sign before pulling out, and did not see vehicle #1 until the moment of impact. (From the stop sign, vehicle #2 would have traveled 30 feet to the point of impact.

**After the collision, both vehicles experience wheel lock due to crash damage and skidded over asphalt (μk = 0.72) followed by grass (μk = 0.35).**Neither surface has any significant incline.

**Vehicle #1 skidded on 20 feet of asphalt and 30 feet of grass before coming to rest. The angle of departure for vehicle #1 was 45 degrees north of east.**

The weight of vehicle #1 including occupants was 4300 lbs.**Vehicle #2 skidded on 25 feet of asphalt and 35 feet of grass before coming to rest. The angle of departure for vehicle #2 was 35 degrees north of east.**

The weight of vehicle #2 including occupants was 3150 lbs.

An acceleration test concluded that a vehicle such as vehicle #2 would have a maximum acceleration of 2.0 m/s^2 at the time of the accident.

**What was the speed of each vehicle after the collision?**"

## Homework Equations

(I'm all over the place, but...)

KE = (1/2)(m)(v^2)

W = Fd(cosθ)

W = ΔKE

F(friction) = (μk)(F(normal)) = (μk)(mg)

KE1 + PE1 + W(external) = KE2 + PE2

J = FΔt = mΔv = Δp

p = mv

## The Attempt at a Solution

Originally, I used the fact that the work of friction is equal to the change in kinetic energy, so:

W(f) = ΔKE

(μk)(mg)(d)(cosθ) = (1/2)(m)(v^2)

√[2(μk)(g)(d)(cosθ)] = v

But this doesn't account for the change in surfaces, from asphalt to grass. Also, I'm not even sure if it properly accounts for the two-dimensions of the collision.

I'm aware that this is a 2D elastic collision problem, and understand how to split the x- and y-components of the velocity. However, I don't think I'm approaching this properly.

Any help would be greatly appreciated.

Thank you!