1.

A particle is moving in a plane with velocity given by u = u_(0)i+ (aomega cos omegat)j, where i and are j are unit vectors along x and yaxes respectively. If particle is at the origin at t = 0. (a) Calculate the trajectroy of the particle. (b) Find the distance form the origin at time 3pi//2omega.

Answer» <html><body><p></p>Solution :Given that `u = u_(0)I +(a omega cos omegat)j`, <br/> Hence, velocity along `x`-axis `u_(x) = u_(0) …(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)` <br/> Velocity along `y`-axis `u_(y) = a omega cos omegat …(2)` <br/> We know that `v=(ds)/(dt)` or `s - int v.dt` <br/> So from <a href="https://interviewquestions.tuteehub.com/tag/equations-452536" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATIONS">EQUATIONS</a> (1) and (2), we have <br/> Displacement at time `t` in horizontal direction <br/> `x =int u_(0) dt =u_(0).t ...(3)` <br/> Displacement in <a href="https://interviewquestions.tuteehub.com/tag/vertical-726181" style="font-weight:bold;" target="_blank" title="Click to know more about VERTICAL">VERTICAL</a> direction <br/> `y = int a omega cos omegat = dt a <a href="https://interviewquestions.tuteehub.com/tag/sin-1208945" style="font-weight:bold;" target="_blank" title="Click to know more about SIN">SIN</a> omegat ...(4)` <br/> Eliminating `t` form equaitons (3) and (4) we get <br/> `y =a sin (omegax//u_(0)) ...(5)` <br/> Equations (5) <a href="https://interviewquestions.tuteehub.com/tag/gives-1007647" style="font-weight:bold;" target="_blank" title="Click to know more about GIVES">GIVES</a> the trajectroy of the particle. <br/> (b) At time, `t = 3pi//2 omega` <br/> `x = u_(0) (3pi//2omega)` and `y = a sin 3pi//2 =-a` <br/> `:.` Distance of the particle form teh origin <br/> `=sqrt((x^(2)+y^(2)))=sqrt([((3piu_(0))/(2omega))^(2)+a^(2)])`</body></html>


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