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 = 42 m/s. The third piece has three times the mass of the other two pieces. Randomized Variables V = 42 m/s show answer No Attempt 33% Part (a) Write an expression for the speed of the larger piece, that is in terms of only the variable V.

Speed of larger piece is

Explanation:

We apply the principle of conservation of momentum.

The watermelon is initially at rest. The initial momentum = 0 kg m/s in all directions.

After the collision,

Vertical momentum = momentum of piece in y-direction + y-component of momentum of larger piece =

Here, is the y-component of velocity of larger piece.

This is equal to 0, since the initial momentum is 0.

Horizontal momentum = momentum of piece in x-direction + x-component of momentum of larger piece =

Here, is the x-component of velocity of larger piece.

This is also equal to 0, since the initial momentum is 0.

The velocity of the larger piece, , is the resultant of and . Since they are mutually perpendicular,

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