Question

Problem 9.41

A firecracker in a coconut blows the coconut into three pieces. Two pieces of equal mass fly off south and west, perpendicular to each other, at 20 m/s . The third piece has twice the mass as the other two.

Part A

What is the speed of the third piece?

Express your answer using two significant figures.

Part B

What is the direction of the third piece? Give the direction as an angle east of north.

Express your answer using two significant figures.

Answer 1

so you know the first and second pieces are going both south and west,
you know the third must then balance these two directions are momentum is conserved.
meaning its the exact opposite of the two directions, being 45 degrees North of East.
thats basically how i figured it anyways, and thats the right answer. from there you know
your going to deal with two pieces to find the speed. because when you look at it, the first and second piece either move in the x or y direction. not both, except for your third piece.
now, by trial and error you find that you will use the piece travelling in the y direction as you need to use an angle later on, and the x direction's angle would be cos90, giving you zero, which does not give you an answer.. so, use the y direction
because your not given mass leave them as m1 and m3 or m2 m3 however you labelled your diagram.

then you do the original mv y = m1v1y + m3v3y to show momentum in the y direction and that it is conserved.

you then set it to 0 as your original coconut is not moving.

so it looks like 0=m1v1y + m3v3y

then get slightly more specific as you have labelled your diagram one of these v's are negative
=(m1)(-v1) + (m3)(v3)

you also know that m3 or the third piece's mass is twice that of the first so then
=(m1)(-v1) + (2m1)(v3)

from there begin to sub in values, sin 45 comes from the 45 degree angle already found and sin is used as we are using the y direction
=(1)(-18)(sin90) + (2)(v3)(sin45)

=-18 +(2)(v3)(sin45)

begin to solve
18/2=(v3)(sin45)/2

v3=9/(sin45)

v3=12.72792206
v3=13m/s