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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

m_a u_a = m_av_a Cos 25 + m_b v_b Cos 65

4.2 = 0.91v_a + 0.42v_b ----- 1

Along y axis

0 = m_av_a Sin 25 - m_b v_b Sin 65

0.42 v_a = 0.91 v_b

or v_a = 2.17v_b

substituting in eq 1 and solving we get

v_b = 1.75 m/s

hence v_a = 2.17 v_b = 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?