The position of a particle at any instant is given by r = 5t² i + 50t j. At what instant the velocity    vector will make an angle 45° with X-axis. 

Asked by debjit_dm | 15th Apr, 2020, 10:13: PM

Expert Answer:

Position vector begin mathsize 14px style r with rightwards arrow on top end style is given by
begin mathsize 14px style r with rightwards arrow on top space equals space 5 t squared space i with hat on top space plus space 50 space t space j with overbrace on top end style  .......................(1)
velocity vector is obtained by differentiating eqn.(1)
 
begin mathsize 14px style v with rightwards arrow on top space equals space fraction numerator d space r with rightwards arrow on top over denominator d t end fraction space equals space 10 space t space i with hat on top space plus space 50 space j with hat on top space end style
if velocity vector makes angle 45o with x-axis means, x-component of velocity and y-component velocity are equal
 
hence, 10 t = 50  or  t = 5 s

Answered by Thiyagarajan K | 15th Apr, 2020, 11:34: PM

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