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Two masses moving on a frictionless surface approach the origin where they collide. Their initial velocities ( and ) are unknown. After the collision, the masses are joined together in a tangled mess that moves up and to the right with an angle of with respect to the x-axis. 1. What is the ratio of the initial velocities,

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lublana

Answer:

1.07

Explanation:

Let m1 and m2 be two masses moving with initial velocity v1 and v2.

[tex]\theta=25^{\circ}[/tex]

[tex]m_1=2m[/tex]

[tex]m_2=m[/tex]

According to law of conservation of momentum

Along x- axis

[tex]m_1v_1+0=(m_1+m_2)cos25[/tex]

[tex]2mv_1=3mcos25[/tex]..(1)

Along y- axis

[tex]0+mv_2=3msin25[/tex]

[tex]mv_2=3msin25[/tex]....(2)

Equation (1) divided by equation (2)

[tex]\frac{2v_1}{v_2}=cot 25=2.14[/tex]

[tex]\frac{v_1}{v_2}=\frac{2.15}{2}=1.07[/tex]

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