Question

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)?

Answer 1

25 m/s

Step-by-step 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:

`m_1*v_1=m_3*v_(3y)\\0.2*40=0.4*v_(3y)\\v_(3y)=20\ m/s`

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

`m_2*v_2=m_3*v_(3x)\\0.3*20=0.4*v_(3x)\\v_(3x)=15\ m/s`

The speed of the last piece is:

`v_3^2 = v_(3y)^2+v_(3x)^2\\v_3=√(20^2+15^2)\\v_3=25\ m/s`

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