Question

Two automobiles, each of mass 1000 kg, are moving at the same speed, 20 m/s, when they collide and stick together. In what direction and at what speed does the wreckage move a) if one car was driving north and one south and b)if one car was driving north and one east?

Answer 1

Answer

given,

mass of  two automobile = 1000 kg

speed of the two automobile = 20 m/s

let north be +y direction and east be +x directon.

a) from momentum conservation

m₁ v₁ + m₂ v₂ = (m₁ + m ₂) v

1000 × 20 - 1000 ×20 = (1000 + 1000)× v

  v = 0 m/s  [no direction]

b) from moment of momentum conservation in x-direction

  1000 × 20 =  (1000 + 1000)× v _x

               v_x = 10 m/s

   from moment of momentum conservation in x-direction

   1000 × 20 =  (1000 + 1000)× v _y

               v_y = 10 m/s

        Resultant = $\sqrt{10^2+10^2}$

                         = 14.14 m/s

   $tan \theta = \dfrac{10}{10}$

     $tan \theta = 1$

         $\theta = 45^0$