Expert Witness Testimony: Accident Analysis

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In the accident analysis case, car A collided with car B while sliding down a hill with a slope of 12.0°. The initial speed of car A was 17.5 m/s, and the distance between the cars was 23.5 m. The coefficient of kinetic friction was considered at two values: 0.60 for a dry road and 0.10 for a wet surface. The calculation for part (a) yielded an incorrect speed of 5.476 m/s due to neglecting the effect of the hill's slope on the frictional force. The user resolved the issue by recognizing the need to account for the slope in their calculations.
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Homework Statement



You testify as an "expert witness" in a case involving an accident in which car A slid into the rear of car B, which was stopped at a red light along a road headed down a hill. You find that the slope of the hill is θ = 12.0°, that the cars were separated by distance d = 23.5 m when the driver of car A put the car into a slide (it lacked any automatic anti-brake-lock system), and that the speed of car A at the onset of braking was v0 = 17.5 m/s.

(a) With what speed did car A hit car B if the coefficient of kinetic friction was 0.60 (dry road surface)?

(b) What was the speed if the coefficient of kinetic friction was 0.10 (road surface covered with wet leaves)?

Homework Equations



∑F = ma = μmg

v² = v₀² + 2aΔx

The Attempt at a Solution



∑F = ma = μmg
a = μg
= 0.600(-9.80m/s²)
= -5.88m/s²

v² = v₀² + 2aΔx
= (17.5m/s)² + 2(-5.88m/s²)(23.5m)
= 5.476m/s (part a)

haven't tried part b

How is this wrong? My online homework said 5.467 wasn't the answer for part a.
 
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InsTanCeZ said:

Homework Statement



You testify as an "expert witness" in a case involving an accident in which car A slid into the rear of car B, which was stopped at a red light along a road headed down a hill. You find that the slope of the hill is θ = 12.0°, that the cars were separated by distance d = 23.5 m when the driver of car A put the car into a slide (it lacked any automatic anti-brake-lock system), and that the speed of car A at the onset of braking was v0 = 17.5 m/s.

(a) With what speed did car A hit car B if the coefficient of kinetic friction was 0.60 (dry road surface)?

(b) What was the speed if the coefficient of kinetic friction was 0.10 (road surface covered with wet leaves)?

Homework Equations



∑F = ma = μmg

v² = v₀² + 2aΔx

The Attempt at a Solution



∑F = ma = μmg
a = μg
= 0.600(-9.80m/s²)
= -5.88m/s²

v² = v₀² + 2aΔx
= (17.5m/s)² + 2(-5.88m/s²)(23.5m)
= 5.476m/s (part a)

haven't tried part b

How is this wrong? My online homework said 5.467 wasn't the answer for part a.
It has to to do with you neglecting the slope of the road.
 
Thanks, I figured it out. :)
 
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