Two cars, both of mass m , collide and stick together. Prior to the collision, o

ID: 1777928 • Letter: T

Question

Two cars, both of mass m , collide and stick together. Prior to the collision, one car had been traveling north at speed 2v , while the second was traveling at speed v at an angle south of east (as indicated in the figure). After the collision, the two-car system travels at speed v final at an angle east of north.

What is the angle with respect to north made by the velocity vector of the two cars after the collision?

Express your answer in terms of . Your answer should contain an inverse trigonometric function using the notation asin, atan etc. and not arcsin, arctan etc.

Explanation / Answer

The vertical component of vfinal is related by
2*v*m-v*m*sin()=2*m*vfinal*cos()

and the horizontal is
v*m*cos()=2*m*vfinal*sin()

divide the two equations to get
tan()=cos()/(2-sin())

=> = atan(cos/(2-sin)

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Two cars, both of mass m , collide and stick together. Prior to the collision, o

Two cars, both of mass m, collide and stick together. Prior to the collision, on

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Two cars, both of mass m , collide and stick together. Prior to the collision, o

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