(10%) Problem 3: A car with mass me-1267 kg is traveling west through an interse

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(10%) Problem 3: A car with mass me-1267 kg is traveling west through an intersection at a magnitude of velocity of vc -13 m/s when a truck of mass m 1961 kg traveling south at vt 7.2 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 ?,-0.5 Otheexpertta.com 50% Part (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 50% Part (b) How far, in meters, will the vehicles slide after the collision? Grade Summary Deductions Potential 3% 97% sin Submissions Attempts remaining: 2 (190 per attempt) detailed view 78 9 cotanasin0 acos0 sinhO atanOacotan) si 1% 11% 1% cosh0tan0 coho 0 END Degrees Radians Submit Hint Hints: 1 % deduction per hint. Hints remaining: 1 Feedback: 0% deduction per feedback Submission History All Date times are displayed in Eastern Standard Time Red submission date times indicate late work Hints Answer d 6.722 d 6.65 d 6.67 Feedback 1 2 3 Date Jul 23, 2018 Jul 23,2018 Jul 24,2018 4:24 PM 4:31 PM 1:17 PM

Explanation / Answer

given mass of car mc = 1267 kg

vc = 13 m/s

mt = 1961 m/s

vt = 7.2 m/s

given perfectly inelastic collision

asphalt coefficient of friction, uk = 0.5

a. rom the given data, using conversation of momentum

let the final velocity of the two objects be v

then

mt*vt + mc*vc = (mt + mc)* v

v = (mt*vt + mc*vc)/(mt + mc)

using vectors

v = (1961*(-7.2) j + 1267*(-13) i)/(1961 + 1267) = 5.10254i -4.373977j m/s

b. KE of the system just after collision = 0.5(mt + mc)*v^2 = 72900.49353671 J

from work energy theorem

KE = uk*(mt + mc)*g*d

where d is sliding distance

d = 4.60423 m

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