A 4.0 kg mess kit sliding on a frictionless surface explodes into two 2.0 kg parts: 3.0 m/s, due north, and 5.0 m/s, 30° north of east. What is the original speed of the mess kit?

3.49m/s

Explanation:

We have mess of kit = 4kg

Then pieces are 2kg

3m/s due north

5m/s, 30⁰ due south

MiVi = m1v1 + m2v2

We break velocities to have x and y components

MiVi = m1v1(cosθ+sin θ1j) + m2v2(v2cos θ2i+sin2 θj)

θ1 = 90⁰north

θ2 = 30⁰ north east

Vi = 2/4x3m/s(cos90i + sin90j)+2/4x5m/s(cos30i + sin30j)

= 2.16i + 2.75j

Vi = √Vx²+Vy²

Vi = √ (2.16)²+(2.75)²

Vi = 3.49m/s

This is the original speed of the kit