Question

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 = 23 m/s. The third piece has three times the mass of the other two pieces.
Write an expression for the speed of the larger piece, that is in terms of only the variable V.

What is the numeric value for the speed of the larger piece, in meters per second?

At what angle does the largest piece travel with respect to the -y axis, in degrees?

Answer 1

(a) The expression for the speed of the larger piece is $\frac{v\sqrt{2} }{3}$.

(b) The numeric value for the speed of the larger piece is 10.84 m/s.

(c) The direction of the larger piece is 45⁰ with respect to y - axis.

Expression for the speed of the larger piece

Apply the principle of conservation of linear momentum;

m₁v₁ + m₂v₂ + m₃v₃ = 0

where;

• m₁ is mass of first piece
• m₂ is mass of second piece
• m₃ is mass of third piece = three times the mass of other piece = 3m

mv.i + mv.j + (3m)v₃  = 0

(3m)v₃  = -mv.i - mv.j

3v₃ = - v.i - v.j

$v_3 = \frac{-v_i \ - \ v_j}{3} = \frac{v\ (\sqrt{(-1)^2 + (-1)^2} )}{3} = \frac{v\ \sqrt{2} }{3}$

Numeric value for the speed of the larger piece

$v_3 = \frac{23 \times \sqrt{2} }{3} \\\\v_3 = 10.84 \ m/s$

Direction of the larger piece

tan θ = vj/vi

tan θ = 1/1

tan θ = 1

θ = arc tan(1)

θ = 45⁰

Learn more about linear momentum here: brainly.com/question/7538238

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