Calculate Speed of Light & Heavier Car After Collision at Intersection

[bobby3280]

A police officer is investigating the scene of an accident where two cars collided at an intersection. One car with a mass of 1135 kg moving west had collided with a 1300 kg car moving north. The two cars, stuck together, skid at an angle of 30° north of west for a distance of 25 m. The coefficient of kinetic friction between the tires and the road is 0.80.

What was the speed of the lighter car?
______ km/h
What was the speed of the heavier car?
______ km/h

I know this is a perfectly inelastic collistion and that Vf will be equal.
so x-dir m1vi1 = (m1 + m2) Vf cos 30
y-dir m2vi2 = (m1 + m2) Vf sin 30
so i can't solve too many unknowns.
How do i use the 25m and kinetic friction??

 

[Doc Al]

How do i use the 25m and kinetic friction??

Use this info to find the acceleration during the skid and then the speed of the cars immediately after the collision. Hint: What's the force of kinetic friction?

 

[bobby3280]

F = .8 m g
F = .8 * 2435 * 9.8
F = 19090.4 N

a = F/m
a = 19090.4 / 2435
a = 7.84 m/s

I think this is right but not sure after.

Vf^2 - Vi^2 = 2ax
setting Vf to 0 I get a Vi = 19.8
and i know this Velocity is too slow?

 

[Doc Al]

F = .8 m g
F = .8 * 2435 * 9.8
F = 19090.4 N

a = F/m
a = 19090.4 / 2435
a = 7.84 m/s

I think this is right but not sure after.

All good. (Acceleration has units of m/s^2, not m/s.)

Vf^2 - Vi^2 = 2ax
setting Vf to 0 I get a Vi = 19.8
and i know this Velocity is too slow?

What makes you think this is too slow? (Convert to miles/hour to compare with typical speeds.)

 

[bobby3280]

The last part of the question states The speed limit for each car was 70 km/h. And I know that only the lighter car was speeding.

So V1i > 70 km/s

When i solve for my initial velocities using 19.8 and this formula
V1i = ((m1 + m2) / m1) Vf cos 30 putting in 19.8 i get
V1i = 36.8 km/s

Which is considerably lower that 70 km/s

So either my formula or my Vf is wrong but after many hours I still can't find where I'm wrong. Any other help? Thanks so far.

 

[Doc Al]

check your units!

The speed limit is 70 km/hr, not 70 km/s.

Also, standard units will give the speed in m/s, not km/s.

 

[bobby3280]

Wow don't know how i missed that but thanks alot!