A bird moves from a point (1,-2,3) to (4,2,3).If the speed of the bird is 10 m/s, then the velocity vector of the bird is?

1 Answer
Jul 18, 2017

Initial position vector of the bird vecr_i=hati-2hatj+3hatkri=ˆi2ˆj+3ˆk

Final position vector of the bird vecr_f=4hati+2hatj+3hatkrf=4ˆi+2ˆj+3ˆk

So displacement vector

vecd=vecr_f-vecr_id=rfri

=(4hati+2hatj+3hatk)-(hati-2hatj+3hatk)=(4ˆi+2ˆj+3ˆk)(ˆi2ˆj+3ˆk)

=3hati+4hatj=3ˆi+4ˆj

Unit displacement vector

=(vecd)/abs(vecd)=dd

=(3hati+4hatj)/abs(3hati+4hatj)=3ˆi+4ˆj3ˆi+4ˆj

=(3hati+4hatj)/sqrt(3^2+4^2)=3ˆi+4ˆj32+42

=(3hati+4hatj)/5=3ˆi+4ˆj5

The direction of velocity is same as that of displacement.

And the magnitude of velocity is 10m"/"s10m/s

Hence the velocity vector

vecv=10xx(3hati+4hatj)/5v=10×3ˆi+4ˆj5 m/s

=>vecv=6hati+8hatjv=6ˆi+8ˆj m/s