Initial velocities of a snowmobile collision

[tawrper]

Homework Statement

A police officer arrives at the scene of a collision of the two snowmobiles to find both drivers unconscious. When two vehicles collided, their skis became entangled and the two snowmobiles remained locked together as they skidded to a stop. One driver was thrown clear of the mishap, but the other driver remained in the drivers seat. The posted speed limit in the area is 60km/h. One witness described how driver A was thrown horizontally at a constant speed from his seat (0.5 m above the snow surface) to his final resting position.

the initial angle between driver A and Driver B is 30 degrees

Driver A was thrown 8m

Mass of Driver A 80kg

Mass of driver B 90kg

Mass of vehicle A 270 kg

Mass of vehicle B 310kg

Before collision: Vehicle B East30degrees North Vehicle A East

Direction of entangles vehicles after collision East 15 degrees North

length if final skid 18m

displacement of driver A from point of impact: 8m

Time from impact to end skid 2.5s

I need to determine the initial velocities of both snowmobiles.

here is a picture of the question:

Homework Equations

mv1 + mv2 = mv1' + mv2

The Attempt at a Solution

driver a: 670 kg x 25.92 km/h / 350 = 49.62 km/h

driver b: 670 kg x 25.92 km/h / 400 = 43.416 km/h

i know its very wrong, its just an attempt. i really need a lot of help

 

[anathema]

Thank you for your forum post and for providing all of the relevant information and equations. I can see that you have made an attempt at solving the problem, but as you noted, your answer is not correct. I will guide you through the correct approach to solving this problem.

First, we need to use conservation of momentum to find the initial velocities of both snowmobiles. This means that the total momentum before the collision must equal the total momentum after the collision. We can write this as:

(mA + mB)vinitial = (mA + mB)vfinal

Where mA and mB are the masses of the two snowmobiles and vinitial and vfinal are their initial and final velocities, respectively.

Next, we need to find the initial velocities of the snowmobiles. We can do this by using the information given in the problem and some basic trigonometry. We know that the initial angle between the two snowmobiles is 30 degrees. This means that the components of their velocities in the x-direction (east) and y-direction (north) will be:

vAx = vinitial cos(30) = vinitial * √3/2

vAy = vinitial sin(30) = vinitial * 1/2

vBx = vinitial cos(30) = vinitial * √3/2

vBy = vinitial sin(30) = vinitial * 1/2

Using this information, we can rewrite our conservation of momentum equation as:

(mA + mB)(vinitial * √3/2) = (mA + mB)(vfinal * √3/2)

Simplifying, we get:

vinitial = vfinal

This means that the initial and final velocities of both snowmobiles will be the same. Now, we can use the information given in the problem to solve for the final velocity. We know that the length of the final skid is 18m and the time from impact to end of skid is 2.5s. This means that the final velocity will be:

vfinal = 18m / 2.5s = 7.2 m/s

Now, we can plug this value into our conservation of momentum equation to solve for the initial velocity of both snowmobiles. We get:

(mA + mB)(vinitial * √3/2) = (mA