A 950 kg eastbound van full of peanut butter collides with a 1430 kg northbound

Question

A 950 kg eastbound van full of peanut butter collides with a 1430 kg northbound truck full of jelly. The two vehicles lock fenders, and skid off together. The accident reconstruction team observes that the skid marks created by the vehicles after the collision are 11 m long, directed at an angle 62° north of due east. They also know that, under the driving conditions at the time of the accident, the coefficient of kinetic friction on the road was 0.84.

Determine the speed of each vehicle prior to the collision.
Van: ___________m/s
Truck: __________m/s

(You may assume that the jelly was seedless strawberry, and that the peanut butter was chunky-style.)

Explanation / Answer

lets assume before accident,
velocity of peanut butter van = v1 i m/s
velocity of jelly truck = v2 j m/s
after collision they goes to 11m together,
they is only friction force to stop it ,
so f = ma

.mg = ma

a = g = 0.84 X 9.81 = 8.24 m/s2

v2 - u2 = 2as

0 - u2 = 2(-8.24)(11)

u = 13.46 m/s

ux = 13.46cos62 = 6.32 i

uy = 13.46sin62 = 11.88 j

so by the conservation of momentum just during the collision,

950 X v1i + 1430 X v2j = (950+1430) X (6.32i + 11.88j)

v1 = 2380 X 6.32 / 950 = 15.83 m/s towards east

v2 = 2380 X 11.88 / 1430 = 19.77 m/s towards north

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