Question

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with velocity 12 ms1 and 2 kg, second part moving with velocity of 8 ms1. If the third part flies off with a velocity of 4 ms1, its mass would be

Answer 1

Answer:

The mass of the third part would be 5 kg.

Explanation:

Initially the object is at rest. So, its net initial momentum Pi is zero. Which means, its net final momentum Pf will also be zero. So, we have;

                Pi = Pf = 0

Now, Let the mass 1 kg be m₁, mass 2 kg be m₂ and third part's mass be m₃. Let the velocities be v₁, v₂ and v₃ of the given masses in that order. Now we have;

                     Pi = Pf = 0

                      Pf = 0

      m₁v₁ + m₂v₂ + m₃v₃ = 0

            m₁v₁ + m₂v₂ = -m₃v₃

       (12×1)i + (2×8)j = - m₃ (4)

(Refer to the attached image for the visualization)

                  20 = - 4 m₃

                   5 = - m₃  (since mass can't be negative)

              m₃ = 5 kg

Hope it helps! ;-))