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frensel
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Homework Statement
As shown in the figure below, a particle is moving in a circle of radius [itex]R[/itex] with constant speed [itex]v[/itex]. At some location, the particle is detached from the circle and falls with a parabola path to point A. What is the horizontal range [itex]x[/itex] of the projectile?
Homework Equations
Writing the kinematic formula in component form, we have
$$x=v\sin(a)t$$
$$h-y=v\cos(a)t+\frac{1}{2}gt^2$$
and using Pythagorean theorem, we get
$$R^2=x^2+y^2$$
Since [itex]\sin(a)=y/R, \cos(a)=x/R[/itex], the first and second equations become
[tex]x=\frac{vyt}{R}[/tex]
$$h-y=\frac{vxt}{R}+\frac{1}{2}gt^2$$
The Attempt at a Solution
I have tried to solve the above three equations, but they are too difficult to solve. Some cubic functions will appear and it seems too complicated to be a validated way to solve this problem.
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