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A point p is moving along a circle with equation x^2+y^2=100 at a constant rate of 3 units/sec.?
How fast is the projection of p on the x-axis moving when p is 5 units above the x-axis
2 réponses
- Ian HLv 7il y a 4 ans
When P is 5 units above the x-axis it is moving at 3 units/sec tangentially
x^2 + y^2 = 100
2x + 2ydy/dx = 0
Slope at p is –x/y
When y = 5, x = 5√(3)
Slope is - √(3) = tan(θ)
The component along the x-axis employs cos(θ) = 1/2
Speed projection is -3 cos(θ) = -1.5 units/sec
- ?Lv 5il y a 4 ans
y = 5 => x = √(100 - 5²) = 5√3, which means that the angle the circle's radius to this point makes with the x axis is 30°. Since the motion is perpendicular to this radius, the absolute values of its vertical and horizontal components must be in the ratio √3:1, where their resultant has a ratio-magnitude of 2, so the x component is half this, or 1.5 units/sec.
