Initial velocity of a snowmobile collision

[tawrper]

Hey everyone;



I am a grade 12 student and I am totally stuck on this question and would appreciate your help. I don't want just the answer, I need help with the steps so that I understand how to do this type of problem.



Here's the question:

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:

Thank you so much in advance. Again, I'm not fishing for answers, I'm in grade 12 and what i don't learn will come back to haunt me in university

 

[NobodySpecial]

Momentum (mass*velocity) is conserved
Consider the momentum in X and y separately

 

[K^2]

There are 3 parts to this problem.

1) Assuming constant deceleration, you can find post-collision velocity of the two snowmobiles. You know the distance they traveled and the time. That should give you deceleration rate and initial velocity.

2) You can find driver A's post-collision velocity by computing time it took him to fall 0.5m to hit snow surface, and knowing that in that time he traveled 8m find velocity.

3) Using the fact that momentum is conserved in x and y directions, you should be able to write two equations of the form momentum-before = momentum-after and solve them to find the two unknowns: velocities of snowmobiles A and B.

I would imagine that you should be capable of carrying out each of these steps individually, but let us know if you have difficulties with any of them.

 

[tawrper]

There are 3 parts to this problem.

1) Assuming constant deceleration, you can find post-collision velocity of the two snowmobiles. You know the distance they traveled and the time. That should give you

velocity = displacement/time

the given time is 2.5s, and the given distance is 18 m. Wouldn't this give me the final velocity of once the two vehicles are connected and not the individual velocities?

 

[K^2]

Yes, that will give you velocity once they are connected, which you need for the 3rd step.

But you are computing it wrong. Distance/time gives you average velocity. You know that the snowmobiles were slowing down, because they came to a stop. So you should be using a formula that involves acceleration.

 

[tawrper]

thank you, I now understand that we are supposed to use the kinematic equations to determine step 1. Are we supposed to use the equations to determine step 2?