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The motion of a particle is defined by t...

The motion of a particle is defined by the position vector
`vec(r)=(cost)hat(i)+(sin t)hat(j)` Where `t` is expressed in seconds. Determine the value of `t` for which positions vectors and velocity vector are perpendicular.

A

`1` sec

B

`2` sec

C

for all value of `t`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`vec(v)=(dvecr)/(dt)=-sinthat(i)+costhat(j)`
Here `vec(r).vec(v)=0` so `vec(r)botvec(v)` for all `t`.
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