Question 1199547
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A point travels as described by the following parametric equations x = 10t+10cos(3.14t), y = 20t+10sin(3.14t) and z=30t, 
where x,y,z, are in meters, t in seconds, all angles in radians. The vector locating the body at any time is r = ix+jy+kz. 
Determine the magnitude of the velocity of the body in meters per second at time t = 0.75 second.
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        In opposite to the long unreadable solution by @CPhill, 

        I will give the solution in simple readable human form.



<pre>
The components of velocity at t = 0.75 seconds are

    x'(0.75) = {{{10 - 10*3.14*sin(0.75*pi)}}} = {{{10 - 10*3.14*(sqrt(2)/2)}}} = -12.20315293  m/s;


    y'(0.75) = {{{20 + 10*3.14*cos(0.75*pi)}}} = {{{20 - 10*3.14*(sqrt(2)/2)}}} = -2.203152929  m/s;


    z'(0.75) = 30  m/s.


The magnitude of the velocity is


    |V| = {{{sqrt((-12.20315293)^2 + (-2.203152929)^2 + 30^2)}}} = {{{sqrt(1053.770824)}}} = 32.46 m/s.    <U>ANSWER</U>
</pre>

Solved.