Discussion Forum

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 

Answer:

Explanation:

 Given,

   $x= a \cos t$

  $y=a \sin t$

and z=t

 Path is circular in xy-plane,

  $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{a^{2}}= \cos^{2} \theta+\sin^{2} \theta$

   $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$

 In one revolution, the particle moves a distance of unit along x-axis 

 $\frac{dz}{dt}=1$

 Hence, the path is a helix