Two cars get into a minor \"fender bender\" during the rush before 9 am classes

Question

Two cars get into a minor "fender bender" during the rush before 9 am classes at URI. Luckily, no one is injured. Before the collision, car 1 (with mass 814 kg) is going 4.54 m/s towards north on Upper College Road and car 2 (mass 836 kg) is going 6.05 m/s east on Campus Road. Define north as the positive y direction, and east as positive x. At the instant when the cars collide, their collision is the dominant force and you can ignore all external forces so that linear momentum is conserved. The two cars stick together after they collide, in a completely inelastic collision.

A. What is the x component of the two cars' velocity right after the collision? Hints: they stick together, so they act like one object; east will be positive x and west would be negative x. B.What is the y component of the two cars' velocity right after the collision? C. What is the magnitude of the two cars' 2-dimensional velocity right after the collision? Hint: given the answers to parts A and B, this question could be from the vectors section in chapter 1. D.What is the angle between the two cars' 2-dimesional velocity and the x axis (east)?

Explanation / Answer

Applying momentum conservation,

pi = pf

814(4.54j) + (836)(6.05i) = (814 + 836)(v)

v = 3.07i + 2.24 j m/s

(A) vx = 3.07 m/s

(B) vy = 2.24 m/s

(C) v = sqrt(vx^2 + vy^2) = 3.80 m/s

(D) theta = tan^-1(vy/vx) = 36 deg

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