Your friend has had a car accident and is trying to negotiate with the insurance
ID: 1408789 • Letter: Y
Question
Your friend has had a car accident and is trying to negotiate with the insurance company for the other driver that pays for damage to your vehicle. She believes the other car was speeding and also fault the accident was the other driver. She knows that you have the knowledge of physics and hopes he can prove his assertions. She describes her accident scene and tells what happened. She was traveling north when he entered the fateful intersection. There was no stop sign, so she looked in both directions and saw no car approaching. It was a clear, sunny and bright day. When he was in the middle of the intersection, his car was hit by another vehicle driver traveling eastward. The two cars remained united after the collision and skidded to a stop. The speed limit on both roads is 50 mph. Of visible marks on the street, you determine that after the collision the car skidded 56 feet at an angle of 30 degrees north of east before stopping. She has a copy of the police report, which gives the make and year of each car. In the library you determine the weight of the car her friend is 2600 lb and the other car was 2200 lb, including the driver's weight in each case. The coefficient of kinetic friction for rubber skidding on dry pavement is 0.80. It is not enough to prove that the other driver was traveling at excessive speed
Explanation / Answer
speed limit of roads at intersection = 50 mph
= 22.352 m/s
weight of her friend w1 = 2600 lbs
= 11557.532 N
mass of her friend car m1 = 1179.34 kg
weight of other car w2 = 2200 lbs
=16013.5978617 N
mass of other car m2 = 997.9032 kg
after the collision the cars skidded 56 feet at an angle of 30 degress north of east before stopping
from the law of conservation of momentum
m1 u1 = ( m1 + m2 )v cos ...........(1)
1179.34 *u1 = ( 1179.34 + 997.9032) v cos 30
m 2 u2 = ( m1 + m2 ) v sin 30 ...........(2)
997.9032 u2 = ( 1179.34 + 997.9032 ) v sin 30
after the collision the cars skidded 56 feet north of east before stopping
the kinematic equation
v '2 - v 2 = 2 as
The coefficient of kinetic friction of a rubber tire skidding on dry pavement is 0.8
v '2 - v 2 = 2 as
after collision initial speed of cars is
- v2 = 2 ( -g ) s
= 2(0.8*9.8) (17.06 m )
v = 16.355 m /s
initial speed of her car is calculated from equation (1)
1179.34 *u1 = ( 1179.34 + 997.9032) v cos 30
u1 = (1179.34 + 997.9032 )(16.355 m/s ) cos 30 / 1179.34
= 26.1486 m /s
initial speed of other car from eq 2
997.9032 u2 = ( 1179.34 + 997.9032 ) v sin 30
u2 = ( 1179.34 + 997.9032 )(16.355 m/s ) sin 30 / 997.9032
u2 = 17.842 m /s
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