Calvin is up to no good. He drills a small hole into a large turnip and places a small firecracker inside, ignites it and quickly hides behind a tree. When the fire cracker explodes, the turnip splits into three pieces. The first, mass 200 g, shoots straight north with a speed of 40 m/s. The second, mass 300 g shoots straight east with a speed of 20 m/s. The last piece has a mass of 400 g. What are the speed of the last piece (in m/s)?

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pedrocarratore pedrocarratore · Answer 1 · 2020-03-30T03:27:14+02:00

Answer:

25 m/s

Explanation:

According to the conservation of momentum, the resulting momentum in the vertical and horizontal directions must be zero.

At the north/south direction, conservation of momentum states:

[tex]m_1*v_1=m_3*v_{3y}\\0.2*40=0.4*v_{3y}\\v_{3y}=20\ m/s[/tex]

At the East/west direction, conservation of momentum states:

[tex]m_2*v_2=m_3*v_{3x}\\0.3*20=0.4*v_{3x}\\v_{3x}=15\ m/s[/tex]

The speed of the last piece is:

[tex]v_3^2 = v_{3y}^2+v_{3x}^2\\v_3=\sqrt{20^2+15^2}\\v_3=25\ m/s[/tex]

The speed of the last piece is 25 m/s.