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.

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adelekeademolu adelekeademolu · Answer 1 · 2020-03-22T04:06:04+01:00

Answer:

Speed of larger piece is [tex]\dfrac{V\sqrt{2}}{3}[/tex]

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 = [tex]mV + 3mv_{ly}[/tex]

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

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

[tex]v_{ly}=\dfrac{V}{3}[/tex]

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

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

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

[tex]v_{lx}=\dfrac{V}{3}[/tex]

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

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

[tex]v_l = \dfrac{V\sqrt{2}}{3}[/tex]