Calculate Speed of Light & Heavier Car After Collision at Intersection

In summary, two cars with masses of 1135 kg and 1300 kg collided at an intersection, skidding 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 was 0.80. The acceleration during the skid was 7.84 m/s^2 and the initial velocity of the cars was 19.8 m/s. The speed limit for each car was 70 km/h and only the lighter car was speeding. The initial velocity of the lighter car was calculated to be 36.8 km/h.
  • #1
bobby3280
12
0
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??
 
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  • #2
bobby3280 said:
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?
 
  • #3
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?
 
  • #4
bobby3280 said:
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.)
 
  • #5
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.
 
  • #6
check your units!

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

Also, standard units will give the speed in m/s, not km/s.
 
  • #7
Wow don't know how i missed that but thanks alot!
 

Related to Calculate Speed of Light & Heavier Car After Collision at Intersection

1. How do you calculate the speed of light?

The speed of light is calculated by dividing the distance traveled by the time it takes to travel that distance. The formula for calculating the speed of light is s = d/t, where s is the speed, d is the distance, and t is the time.

2. How do you calculate the speed of a heavier car after a collision at an intersection?

The speed of a heavier car after a collision at an intersection can be calculated using the conservation of momentum equation, which states that the total momentum before a collision is equal to the total momentum after a collision. The formula is m1v1 + m2v2 = m1v1' + m2v2', where m is the mass and v is the velocity of the objects before and after the collision.

3. What is the speed of light in a vacuum?

The speed of light in a vacuum is approximately 299,792,458 meters per second or 186,282 miles per second. This is the maximum speed at which all matter and information in the universe can travel, according to Einstein's theory of relativity.

4. What factors can affect the speed of a car after a collision at an intersection?

The speed of a car after a collision at an intersection can be affected by factors such as the mass and velocity of the cars involved, the angle of collision, the presence of external forces like friction, and the elasticity of the materials involved in the collision.

5. How does the speed of light compare to the speed of a car after a collision at an intersection?

The speed of light is significantly faster than the speed of a car after a collision at an intersection. The speed of light is constant and is the fastest speed possible, while the speed of a car after a collision is dependent on various factors and is much slower in comparison.

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