Problem 7: A car with mass = 1265 kg is traveling west through an intersection a

Question

Problem 7: A car with mass = 1265 kg is traveling west through an intersection at a magnitude of velocity of vc =13 m/s when a truck of mass mt = N(y) 1590 kg traveling south at vt = 9.6 m/s fails to yield and collides with the car. The vehicles become stuck together and slide on the asphalt, which has a coefficient of friction of Mk = 0.5. Randomized Variables (a) Write an expression for the velocity of the system after the collision, in terms of the variables given in the problem statement and the unit vectors i and j. Part (b) How far, in meters, will the vehicles slide after the collision?

Explanation / Answer

Here , let the final velocity of system is v

a) as there is no external force acting on the system during the collision ,

the momentum of the system befoe and after the collision will be conserved

initial momentum = final momentum

v *(mc + mt) = - mc * vc i - mt * vt j

v = - (mc * vc i + mt * vt j )/(mc + mt)

the expression of the final velocity is - (mc * vc i + mt * vt j )/(mc + mt)

b)

putting value in expression

v = - (mc * vc i + mt * vt j )/(mc + mt)

v = - (1265 * 12 i + 1590 * 13 j )/(1265 + 1590)

v = - (1265 * 12 i + 1590 * 13 j )/2855

v = -5.87 i - 7.24 jm/s

speed , v = sqrt(5.87^2 + 7.24^2)

v = 9.32 m/s

due to friction , acceleration = -u*g

acceleration = - 0.5 * 9.8

acceleration = -4.9 m/s^2

Now , for the distance slided by the vehicles

d = v^2/(2 * a)

d = 9.32^2/(2 * 4.9)

d = 8.86 m

the vehicles will slide 8.86 m

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