Your friend has just been in a traffic accident and hopes that you can show the

Question

Your friend has just been in a traffic accident and hopes that you can show the accident was the other driver?s fault. Your friend?s car was traveling North when it entered the intersection. When it reached the center of the intersection, the car was struck by the other driver?s car which was traveling East. The tow cars remained joined together after the collision and skidded to a stop. The speed limit on both roads is 50 mph From the skid marks still visible on the street, you determine that after the collision the cars skidded 56 feet at an angle of 30 degrees north of east before stopping. The weight of your friend?s car is 2600 lbs and that of the other car is 2200 lbs. The coefficient of kinetic friction for a rubber tire skidding on dry pavement is 0.80. You decide to see if the other driver was speeding. mi/hr

Explanation / Answer

we know from eqn of motion

v^2 = u^2 + 2 a s

a = ug = 0.8 x 9.81 = 7.85 m/s^2 ; s = 56 ft = 17.07 m

v = sqrt (2 x 7.85 x 17.07) = 16.37 m/s

m1 = 2600 lbs = 1179.34 kg ; m2 = 2200 lbs = 998

from conservation of momentum

Pi = Pf

m1u1 = (m1 + m2)v cos(theta) In x direction

m2u2 = (m1 + m2)v sin(theta) In y direction

u1 = (m1 + m2) v cos(theta)/m1

u1 = (1179.34 + 998)/1179.34 x 16.37 x cos30 = 26.17 m/s = 58.54 mi/h

u2 =(1179.34 + 998)/998 x 16.37 x sin30 = 17.86 m/s = 39.95 mi/h

the speed of friends car = 58.54 mi/hr

other car = u2 = 39.95 mi/h

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