Question 187: Motion in 2D & Vectors

Question

A particle moves in x-y plane according to rule x = asin$$\omega $$t  and  y = acos$$\omega $$t. The particle follows

Accepted Answer

$$x = a\sin \omega t$$ or $${x \over a} = \sin \omega t$$    ....(1)
$$y = a\cos \omega t$$ or $${y \over a} = \cos \omega t$$    ....(2)
Squaring and adding, we get
$${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{a^2}}} = 1$$    ($$ 	herefore $$ $${\cos ^2}\omega t + {\sin ^2}\omega t = 1$$)
or $${x^2} + {y^2} = {a^2}$$
This is the equation of a circle. Hence particle
follows a circular path.

Answer

an elliptical path

Answer

a circular path

Answer

a parabolic path

Answer

a straight line path inclined equally to x and y-axes

Motion in 2D & Vectors

A particle moves in x-y plane according to rule x = asin$\omega t and y = acos\omega $t. The particle follows

Choose the correct answer: