Question

Consider the motion of a particle described by $x=a\cos t,y=a\sin t$ and $z=t$. The trajectory traced by the particle as a function of time is

• A. Helix
• B. Circular
• C. Elliptical
• D. Straight line

Answer 1

The correct option is A Helix

path is circular in x-y plane
$\frac{x^2}{a^2}+\frac{y^2}{a^2}={\cos }^2\theta +{\sin }^2\theta =1$
$⟹x^2+y^2=a^2$ which is the equation of circle.
In one revolution, the particle moves $A$ distance of $1$ unit along z-axis
$\therefore \frac{dz}{dt}=1$
Thus the particle moves along z direction with constant speed tracing a circular path in xy plane.
Hence the overall path is helix.