A neutron (mass 1.01 u) strikes a deuteron (mass 2.01 u), and they combine to form a tritium nucleus (mass 3.02 u). The neutron's initial velocity was 23.5i^+14.4j^Mm/s and the tritium nucleus leaves the reaction with velocity 15.1i^+22.6j^Mm/s. Select the correct deuteron's velocity. Express your answer in terms of i^ and j^. Use the 'unit vector' button to denote unit vectors in your answer.

Let us form a system constituted by the neutron, deuteron and tritium for this system all the forces during the crash are internal so that the moment is conserved. Let us remember that the moment is a vector quantity, so each component must be kept independent of the others.

We establish a nomenclature

Neutron

mₙ = 1.1 u

vₙ₀ = (235 i ^ 14.4 j ^) 10⁶ m/ s

[tex]m_{D[/tex] = 2.01 u

X axis

p₀ₓ = mₙ vₙ₀ₓ + [tex]m_{D[/tex] [tex]v_{Dox}[/tex]

[tex]p_{fx}[/tex] = [tex]m_{T}[/tex] [tex]v_{Tfx}[/tex]

Axis y

[tex]p_{oy}[/tex] = mₙ [tex]v_{noy}[/tex] + [tex]m_{D[/tex] [tex]v_{Doy}[/tex]

[tex]p_{fy}[/tex] = [tex]m_{T[/tex] [tex]v_{Tfy}[/tex]

Let's write the conservation equations of the moment and solve

p₀ₓ = [tex]p_{fx}[/tex]

mₙn vₙ₀ₓ + [tex]m_{D[/tex] [tex]v_{Dox}[/tex] = [tex]m_{T[/tex] vTfx

[tex]m_{D[/tex] [tex]v_{Dox}[/tex] =[tex]m_{T[/tex] [tex]v_{Tfx}[/tex] - mₙ vₙ₀ₓ

[tex]p_{oy}[/tex] = [tex]p_{fy}[/tex]

mₙ [tex]v_{noy}[/tex] + [tex]m_{D[/tex] [tex]v_{Doy}[/tex] = [tex]m_{T[/tex] [tex]v_{Tfy}[/tex]

[tex]m_{D[/tex] [tex]v_{Doy}[/tex] = [tex]m_{T[/tex] [tex]v_{Tfy}[/tex] - mₙ [tex]v_{noy}[/tex

calculate

2.01u [tex]v_{Dox}[/tex] = 3.02u 15.1 - 1.01u 23.5

2.01 [tex]v_{Dox}[/tex]= 21.867

[tex]v_{Dox}[/tex] = 21.867 / 2.01

[tex]v_{Dox}[/tex]= 10.88 10⁶ m / s

2.01u [tex]v_{Doy}[/tex] = 3.02u 22.6 - 1.01 14.4

[tex]v_{Doy}[/tex] = 54.71 10⁶ /2.01

[tex]v_{Doy}[/tex] = 27.11 10⁶ m/s

okpalawalter8 okpalawalter8 · Answer 2 · 2021-11-19T16:14:23+01:00

We have that for the Question, it can be said that the correct deuteron's velocity is

[tex]v = 10.88i + 26.72j Mm/s[/tex]

From the question we are told

A neutron (mass 1.01 u) strikes a deuteron (mass 2.01 u), and they combine to form a tritium nucleus (mass 3.02 u). The neutron's initial velocity was 23.5i^+14.4j^Mm/s and the tritium nucleus leaves the reaction with velocity 15.1i^+22.6j^Mm/s.

Select the correct d euteron's velocity. Express your answer in terms of i^ and j^. Use the 'unit vector' button to denote unit vectors in your answer.

Generally the equation for the momentum law is mathematically given as

initial=final of the system

[tex](1.01)*(23.5i + 14.4j) + (2.01*v) = (3.02)(15.1i + 22.6j )[/tex]

[tex]v = 10.88i + 26.72j Mm/s[/tex]

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