2) Two vehicles approach a right angle intersection and then collide. After the collision, they become entangled. If their mass ratios were 1: 4 and their respective speeds as they approached were both 13 m/s, find the magnitude and direction of the final velocity of the wreck.

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nuuk nuuk · Answer 1 · 2019-11-06T06:41:22+01:00

Answer:[tex]10.71 m/s at angle of 75.96^{\circ}[/tex]

Explanation:

Given

Given two vehicles approach a right angle

Suppose one is traveling with towards north and other towards east

Ratio of their masses is [tex]\frac{m_1}{m_2}=\frac{1}{4}[/tex]

Both have a common velocity(u) of 13 m/s and v be the final velocity at an angle of [tex]\theta [/tex]w.r.t to east after collision

after collision they both entangled thus

conserving Momentum in east i.e horizontal direction

[tex]m_1u=(m_1+m_2)v\cos \theta [/tex]---1

conserving momentum in North direction i.e. in vertical direction

[tex]m_2u=(m_1+m_2)v\sin \theta [/tex]---2

Divide 1 &2 we get

[tex]\frac{m_1}{m_2}=\frac{\cos \theta }{\sin \theta }[/tex]

[tex]\tan \theta =\frac{m_2}{m_1}[/tex]

[tex]\theta =75.96^{\circ}[/tex] w.r.t east

Thus v is given by

[tex]v\cos (75.96)=\frac{m_1\cdot u}{m_1+m_2}[/tex]

[tex]v\cos (75.96)=\frac{u}{1+4}[/tex]

[tex]v\cos (75.96)=\frac{13}{5}[/tex]

[tex]v=10.71 m/s[/tex]