Question

BEFORE AFTER XV VA e MA VB north east mg [8 pt] The accident. Given your excellent physics legal advice in Worksheet 2-2, you've been asked to make a judgement on another car accident. In this case, a Tesla with mass mA = 2000 kg travelling due east has collided with a Ford F150 Raptor with mass mB = 2500 kg travelling due north. After the collision, it is found that the two vehicles (stuck together) have slid Ax = 7.7 m from the accident site at an angle of 40° north of east (see figure). The car driver claims the accident happened because the truck was speeding; the truck driver claims the car was speeding. The posted speed limit is 35 miles/hour. (a) [4 pt] Work this problem backwards: Determine from the location of the vehicles what the total speed of the car truck system was after the collision. Assume a coefficient of kinetic friction of ulk = 0.90 between the car tire and road surfaces (hint: this is really an energy problem) (6) [4 pt] Now determine the speeds of the car and truck before the collision, assuming it was an inelastic collision. Based on these values, was either car speeding? Who is telling the truth?

Answer 1

x = 7.7 m (after the collision)

coefficient of kinetic friction = 0.9

Therefore, Vf^2 - Uf^2 = 2 ax

0 - Uf^2 = 2 (-0.9*9.8)*7.7

Uf^2 = 135.828

Uf = 11.65 m/s

a) The total speed of car + truck system just after the collision = 11.65 m/s

b) using conservation of momentum along x - axis

2000 * U_a = (2000+ 2500)*11.65*Cos(40 degrees)

U_a = 20.09 m/s

U_a = 44.95 miles/hr   (Speed of car before the collision)

Therefore, car is telling the lie.

Now, conserving the momentum along y - axis

2500 * U_b = (2000+ 2500)*11.65*Sin(40 degrees)

U_b = 13.5 m/s

U_a = 30.2 miles/hr (Speed of truck before the collision)

Therefore, car is telling the Truth.

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