A 1600 kg sedan goes through a wide intersection traveling from north to south w

Question

A 1600 kg sedan goes through a wide intersection traveling from north to south when it is hit by a 2500 kg SUV traveling from east to west. The two cars become enmeshed due to the impact and slide as one thereafter. On-the-scene measurements show that the coefficient of kinetic friction between the tires of these cars and the pavement is 0.750, and the cars slide to a halt at a point 5.60 m west and 6.55 m south of the impact point.

A. How fast was sedan traveling just before the collision?

B. How fast was SUV traveling just before the collision?

Explanation / Answer

distance travelled after collision :

d = sqrt(5.60^2 + 6.55^2)

d = 8.62 m

theta = tan^-1(6.55/5.60) = 49.47 degree

now work = force * distance

W = mu*(1600 + 2500 ) * 8.62 = 259764 J

this is the work done by friction so immediately after the collision this how much kinetic energy tha joined cars had

v = sqrt(2E/m) = 11.26 m/s

1 ) y direction = 1600 * vi = 4100 v*sin49.47

vi = 21.93 m/s

B )

2500 vi = 4100 * v*cos49.47

vi = 12 m/s

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