Question 193: 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: