What Are the Initial Velocities of Snowmobiles in a Collision?

[vintage20]

Help needed -- collision of two snowmobiles

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.

Homework Equations

The Attempt at a Solution

Va: ΔD/ΔV= 8/0.32=25m/s
and
vb= 14.4m/s

 

[anathema]

Thank you for reaching out for help with this collision of two snowmobiles. I can provide some insights and calculations to help determine the initial velocities of both snowmobiles.

First, we need to understand the forces and momentum involved in this collision. From the given information, we know that the two snowmobiles were traveling at the posted speed limit of 60 km/h, which is equivalent to 16.67 m/s. We also know that the two vehicles became entangled and remained locked together, skidding to a stop with a final skid length of 18m.

To determine the initial velocities of the snowmobiles, 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 have two snowmobiles colliding, so we can write the following equation:

(ma * va) + (mb * vb) = (ma + mb) * vf

Where:

ma = mass of vehicle A
mb = mass of vehicle B
va = initial velocity of vehicle A
vb = initial velocity of vehicle B
vf = final velocity of both vehicles (since they are locked together)

We also know that the direction of the entangled vehicles after the collision is East 15 degrees North, which means that the final velocity vector of both vehicles can be broken down into two components: one in the East direction and one in the North direction. Using basic trigonometry, we can calculate the individual velocities in each direction.

East component: vf * cos(15) = 16.67 m/s
North component: vf * sin(15) = 4.24 m/s

Now, let's plug in the given values into our equation:

(270 kg * va) + (310 kg * vb) = (270 kg + 310 kg) * vf

Simplifying and substituting the calculated values for the components of vf, we get:

270va + 310vb = 580 * 16.67
270va + 310vb = 9667.6

We also know that the time from impact to the end of the skid is 2.5 seconds, so we can use the formula for average velocity (v = d/t) to find the average velocity during the skid:

Average velocity = 18m / 2.5s = 7