2D vector Magnitude & Direction:

$\overline{)\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{p}\mathbf{\right|}{\mathbf{=}}\sqrt{{{\mathit{p}}_{\mathbf{x}}}^{\mathbf{2}}\mathbf{+}{{\mathit{p}}_{\mathbf{y}}}^{\mathbf{2}}}}$

$\overline{){\mathbf{tan}}{\mathit{\theta}}{\mathbf{=}}\frac{{\mathit{p}}_{\mathit{y}}}{{\mathit{p}}_{\mathit{x}}}}$

Momentum:

$\overline{){\mathbf{p}}{\mathbf{=}}{\mathbf{m}}{\mathbf{v}}}$

**(a)**

Initial momentum is zero - the watermelon was at rest.

Conservation of momentum along the y-axis:

0 = (mV - (3m)(V_{f})cosθ)j

Conservation of momentum along the x-axis:

0 = (mV - (3m)(V_{f})sinθ)i

Adding the two equations:

A watermelon is blown into three pieces by a large firecracker. Two pieces of equal mass *m* fly away perpendicular to one another, one in the x direction another in the y direction. Both of these pieces fly away with a speed of *V* = *25* m/s. The third piece has three times the mass of the other two pieces.

**Part (a)** Write an expression for the speed of the larger piece, that is in terms of only the variable *V*.

**Part (b)** What is the numeric value for the speed of the larger piece, in meters per second?

**Part (c)** At what angle does the largest piece travel with respect to the -y axis, in degrees?

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