Ah, I get it now.
We know that r(t).r(t)=|r(t)|^2. Differentiating the dot product we get:
d/dt [r(t).r(t)]= 2r'(t).r(t) = 0 (as r'(t) is orthogonal to r(t))
thus |r(t)|^2 is constant, and so |r(t)| is constant, which corresponds to a sphere with the centre at the origin.
Thanks Dick :)
Homework Statement
If a curve has the property that the position vector r(t) is always perpendicular to the tangent vector r'(t) show that the curve lies on a sphere with center at the origin
Homework Equations
The Attempt at a Solution
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Homework Statement
A projectile is fired from the origin down an inclined plane that makes an angle theta with the horizontal. The projectile is launched at an angle alpha to the horizontal with an initial velocity v.
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