A particle moves in space according to the eq | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The position vector is given by $\vec{r} = \sin t \hat{i} + \cos t \hat{j} + t \hat{k}$.The velocity vector is $\vec{v} = \frac{d\vec{r}}{dt} = \c

Vedclass · Accepted Answer

Never

Vedclass · Answer

(D) The position vector is given by $\vec{r} = \sin t \hat{i} + \cos t \hat{j} + t \hat{k}$.The velocity vector is $\vec{v} = \frac{d\vec{r}}{dt} = \cos t \hat{i} - \sin t \hat{j} + 1 \hat{k}$.The acceleration vector is $\vec{a} = \frac{d\vec{v}}{dt} = -\sin t \hat{i} - \cos t \hat{j} + 0 \hat{k}$.For the position vector and acceleration vector to be perpendicular,their dot product must be zero: $\vec{r} \cdot \vec{a} = 0$.Calculating the dot product: $(\sin t)(-\sin t) + (\cos t)(-\cos t) + (t)(0) = 0$.$-\sin^2 t - \cos^2 t = 0$.$-(\sin^2 t + \cos^2 t) = 0$.$-1 = 0$.Since $-1$ can never be $0$,there is no time $t$ for which the vectors are perpendicular. Therefore,they are never perpendicular.

$A$ particle moves in space according to the equation $\vec{r} = (\sin t \hat{i} + \cos t \hat{j} + t \hat{k}) \text{ m}$. Find the time $t$ when the position vector and acceleration vector are perpendicular to each other.

Similar Questions

When a body moves with a constant speed along a circle,

$A$ person is standing on an open car moving with a constant velocity of $30\,m/s$ on a straight horizontal road. The man throws a ball in the vertically upward direction and it returns to the person after the car has moved $240\,m$. Find the speed and the angle of projection.

$A$ particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $\frac{n u^2}{25 g}$,where the value of $n$ is (Given $g$ is the acceleration due to gravity).

$A$ racing car is moving with velocity $v = 40\ m/s$ on a straight track as shown. We are recording it with a camera placed at a distance of $30\ m$ from the road. Find the angular velocity (in $rad/s$) with which we should rotate the camera to record the race at the instant shown in the diagram.

List-$I$ describes four systems,each with two particles $A$ and $B$ in relative motion. List-$II$ gives possible magnitudes of their relative velocities (in $m s^{-1}$) at time $t = \frac{\pi}{3} s$. Which one of the following options is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module