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mr Goodwill [35]
2 years ago
12

Which has more KE ? a 2 g bee flying at 1 m/s OR a 1 g wasp flying at 2 m/s

TexFormula1" title=" \\ " alt=" \\ " align="absmiddle" class="latex-formula"> ty! ~​
Mathematics
1 answer:
nlexa [21]2 years ago
3 0

Answer: Wasp has greater kinetic energy of 0.002 Joules

Given for bee:

  • mass: 2g = 2 × 10⁻³ kg
  • velocity: 1 m/s

Given for wasp:

  • mass: 1 g = 1 × 10⁻³ kg
  • velocity: 2 m/s

Formula:

  • Kinetic Energy (J) = ½ × mass (kg) × velocity² (m/s)

Kinetic energy of bee:

  • ½ × 2 × 10⁻³ × 1² = 1 × 10⁻³ Joules ≈ 0.001 Joules

Kinetic energy of wasp:

  • ½ × 1 × 10⁻³ × 2² = 2 × 10⁻³ Joules ≈ 0.002 Joules

From this, it is determined wasp has greater kinetic energy.

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find the coordinates of the point P on the parabola y=1-x^2 with domain 0≤x≤1 that minimize the area of the triangle enclosed by
coldgirl [10]

Let point P be with coordinates (x_0,y_0). Find the equation of the  tangent line.

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2. The equation of the tangent line at point P is

y-y_0=-2x_0(x-x_0).

Find x-intercept and y-intercept of this line:

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The area of the triangle enclosed by the tangent line at P, the x-axis, and y-axis is

A=\dfrac{1}{2}\cdot (2x_0^2+y_0)\cdot \left(\dfrac{y_0+2x_0^2}{2x_0}\right)=\dfrac{(y_0+2x_0^2)^2}{4x_0}.

Since point P is on the parabola, then y_0=1-x_0^2 and

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Equate this derivative to 0, then

12x_0^4+8x_0^2-4=0,\\ \\3x_0^4+2x_0^2-1=0,\\ \\D=2^2-4\cdot 3\cdot (-1)=16,\ \sqrt{D}=4,\\ \\x_0^2_{1,2}=\dfrac{-2\pm4}{6}=-1,\dfrac{1}{3},\\ \\x_0^2=\dfrac{1}{3}\Rightarrow x_0_{1,2}=\pm\dfrac{1}{\sqrt{3}}.

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Answer: two points: P_1\left(-\dfrac{1}{\sqrt{3}},\dfrac{2}{3}\right), P_2\left(\dfrac{1}{\sqrt{3}},\dfrac{2}{3}\right).

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