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. Two cars 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. After the collision, the two cars stick together and travel off in the direction.
Required:
a. Write the momentum conservation equation for the east-west components.
b. Write the momentum conservation equation for the north-south components.
c. Find the tangent of the angle.

Answer 1

Answer:

a)     vfₓ = m₁ / (m₁ + m₂) v₁,  b)    tan θ  = m₂ / m₁ v₂ / v₁, c)

Explanation:

Momentum is a vector quantity, so the consideration must be fulfilled in all axes

a) conservation of the moment east-west direction

the system is formed by the two cases, so that the forces during the sackcloth have been internal and therefore the mummer remains

before the crash

                 p₀ = m₁ v₁

after the crash

                 $p_{f}$= (m1 + m2) vfₓ

                p₀ = pf

                m₁ v₁ = (m₁ + m₂) vfₓ

              vfₓ = m₁ / (m₁ + m₂) v₁

b) conservation of the North-South axis moment

before the shock

                p₀ = m₂ v₂

after the crash

              p_{f} = ( m₁ +m₂) $vf_{y}$  

             p₀ = p_{f}

            me 2 v₂ = (m₁ + m₂) vfy

       

            $vf_{y}$ = m₂ / (m₁ + m₂) v₂

c) the angle with which the car moves is

             tan θ = Vfy / Vfₓ

             tan θ = [m₂ / (m₁ + m₂) v] / [m₁ / (m₁ + m₂) v₁]

             tan θ  = m₂ / m₁ v₂ / v₁