In this problem we will consider the collision of two cars initially moving at r

Question

In this problem we will consider the collision of two cars initially moving at right angles. We assume that after the collision the cars stick together and travel off as a single unit. The collision is therefore completely inelastic.

The two cars shown in the figure, of masses m1 and m2, collide at an intersection. Before the collision, car 1 was traveling eastward at a speed of v1, and car 2 was traveling northward at a speed of v2. (Figure 1)After the collision, the two cars stick together and travel off in the direction shown.

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1 of 1The figure shows two cars, labeled as car 1 and car 2. Car 1 has mass of m subscript 1 and moves to the east with velocity v subscript 1. Car 2 has mass of m subscript 2 and moves to the north with velocity v subscript 2. There is vector v, starting at the intersection of trajectories of the cars, directed at an angle of theta north of east.

Find the tangent of the angle .

Express your answer in terms of the magnitudes of the initial momenta of the two cars, p1 and p2, or the quantities given in the problem introduction.

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Make sure you have used subscripts where appropriate.

Part C

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Explanation / Answer

V'' = velocity after collision
m1 = mass of car1
m2 = mass of car2
v1 = velocity of mass car 1
v2 = velocity of mass car 2

In elastic collision we have equation.;
m1v1 + m2v2 = (m1 + m2) V'
V' = (m1v1 + m2v2) / (m1 + m2)

B) Momentum equation is given by : p = mv
p1 = m1v1
p2 = m2v2
Because they collide at a right angle
tan = right direction momenta / upward direction momenta
tan = p1 / p2

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