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 17 m/s. The third piece has twice the mass as the other two. Part 1
What is the speed of the third piece?Part 2
What is the direction of the third piece?

12.02 m/s north of east

Explanation:

Let be the horizontal and vertical velocity of the 3rd piece, positive in the East and North direction. Also let m be the mass of the 2 smaller pieces, so 2m is the mass of the 3rd piece.

We can solve for the 2 velocities components using law of momentum conservation. Before the explosion, the total momentum was 0 because the coconut was at rest. After the explosion:

-In the x direction:  

negative 17 because 1 piece flew west

-In the y direction

negative 17 because 1 piece flew south

So the speed and direction of the 3rd piece is

north of east