Answers to Two and Three Dimension of motion Questions

Q
A billiard ball (A) with a mass of 0.165 kg is traveling at 4.2 m/s. It strikes ball B, which is identical to ball A and is stationary. Ball moves on at angle of 25 degrees to the left of its original direction, which ball B moves 65 degrees to the right. a) Draw a vector diagram to show how the law of conservation of momentum could be applied to this situation. b) Write a simplified equation, in terms of mass and the velocity variables, to show how the law of conservation of momentum could be applied to this situation. c) Use the vector diagram and suitable calculation to determine speeds of ball A and ball B after the collision.

Ans

Conservation of momentum will be applied to x and y directions seperately

Along x axis

ma ua = ma va Cos 25 + mb vb Cos 65

4.2 = 0.91va + 0.42vb ----- 1

Along y axis

0 = ma va Sin 25 - mb vb Sin 65

0.42 va = 0.91 vb

or va = 2.17vb

substituting in eq 1 and solving we get

vb = 1.75 m/s

hence va = 2.17 vb = 3.8 m/s

 

Q    Vector A has a magnitude of 25 units and vector B has a magnitude of 15 units.  What is the minimum and maximum magnitude of a vector A + B?


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