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A dinner plate falls vertically to the floor and breaks up into three pieces, which slide horizontally along the floor. Immediately after the impact, a 200-g piece moves along the +x-axis with a speed of 2.00 m/s, a 235-g piece moves along the +y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. What is the speed of the third piece?
a) 2.51 m/s
b) 5.33 m/s
c) 6.83 m/s
d) 2.57 m/s
e) 3.50 m/s

Respuesta :

davidlcastiblanco

Answer:

p_k=\sqrt{p_x^2+p_y^2}}

Explanation:

Apply the momentum in each direction knowing that the impact is at the same time for the pieces so

[tex]p_x=m_1*v_1[/tex]

[tex]p_x=200g*2.0m/s=0.4kgm/s[/tex]

[tex]p_y=m_2*v_2[/tex]

[tex]p_y=235g*1.5m/s=0.3525kgm/s[/tex]

So the momentum in the other piece can be find knowing that

[tex]p_x^2+p_y^2=p_k^2[/tex]

So:

[tex]p_k=\sqrt{p_x^2+p_y^2}}[/tex]

[tex]p_k=\sqrt{0.4^2+0.3525^2}}=\sqrt{0.2842 kg^2*m^2/s^2}[/tex]

[tex]p_k=0.5331kg*m/s[/tex]

To find the velocity knowing the mass

[tex]p_k=m_k*v_k[/tex]

[tex]v_k=\frac{p_k}{m_k}=\frac{0.5331 kg*m/s}{0.10kg}[/tex]

[tex]v_k=5.331 m/s[/tex]

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