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LiRa [457]
3 years ago
14

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.
Physics
1 answer:
Alenkinab [10]3 years ago
3 0

Answer:

Speed of larger piece is \dfrac{V\sqrt{2}}{3}

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 = mV + 3mv_{ly}

Here, v_{ly} is the y-component of velocity of larger piece.

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

v_{ly}=\dfrac{V}{3}

Horizontal momentum = momentum of piece in x-direction + x-component of momentum of larger piece = mV + 3mv_{lx}

Here, v_{lx} is the x-component of velocity of larger piece.

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

v_{lx}=\dfrac{V}{3}

The velocity of the larger piece, v_l, is the resultant of v_{lx} and v_{ly}. Since they are mutually perpendicular,

v_l = \sqrt{v_{ly}^2+v_{lx}^2}= \sqrt{\left(\dfrac{V}{3}\right)^2+\left(\dfrac{V}{3}\right)^2}

v_l = \dfrac{V\sqrt{2}}{3}

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