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A firecracker breaks up into two pieces, one of which has a mass of 200 g and flies off along the x-axis with a speed of 82.0 m/s. The second piece has a mass of 300 g and flies off along the y-axis with a speed of 45.0 m/s. What is the total momentum of the two pieces?

Respuesta :

Answer:

Total momentum, p = 21.24 kg-m/s

Explanation:

Given that,

Mass of first piece, [tex]m_1=200\ g= 0.2\ kg[/tex]

Mass of the second piece, [tex]m_2=300\ g= 0.3\ kg[/tex]

Speed of the first piece, [tex]v_1=82\ m/s[/tex] (along x axis)

Speed of the second piece, [tex]v_2=45\ m/s[/tex] (along y axis)

To find,

The total momentum of the two pieces.

Solve,

The total momentum of two pieces is equal to the sum of momentum along x axis and along y axis.

[tex]p_x=m_1v_1[/tex]

[tex]p_x=0.2\ kg\times 82\ m/s[/tex]

[tex]p_x=16.4\ kg-m/s[/tex]

[tex]p_y=m_2v_2[/tex]

[tex]p_y=0.3\ kg\times 45\ m/s[/tex]

[tex]p_y=13.5\ kg-m/s[/tex]

The net momentum is given by :

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

[tex]p=\sqrt{16.4^2+13.5^2}[/tex]

p = 21.24 kg-m/s

Therefore, the total momentum of the two pieces is 21.24 kg-m/s.