Question

A container explodes and breaks into three fragments that fly off 120° apart from each other, with mass ratios 1: 4: 2. If the first piece flies off with a speed of 6.0 m/s, and the 3rd piece flies off at 3.0 m/s what is the speed of the Second fragments? (All fragments are in the plane.)

Answer 1

Answer:

V₂ = 1.5 m/s

Explanation:

given,

speed of the first piece = 6 m/s

speed of the third piece = 3 m/s

speed of the second fragment = ?

mass ratios = 1 : 4 : 2

fragment break  fly off = 120°

α = β = γ  = 120°

sin α = sin β = sin γ = 0.866

using lammi's theorem

$\dfrac{A}{sin\alpha}=\dfrac{B}{sin\beta}=\dfrac{C}{sin\gamma}$

A,B and C is momentum of the fragments

$\dfrac{m\times 6}{0.866}=\dfrac{4m\times v_2}{0.866}=\dfrac{2m\times 3}{0.866}$

4 x V₂ = 2 x 3

V₂ = 1.5 m/s