A racing car is travelling along a track at a | vedclass

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

Question

(D) Let the distance of the car from the point on the track closest to the camera be $x$. The perpendicular distance from the camera to the track is $

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) Let the distance of the car from the point on the track closest to the camera be $x$. The perpendicular distance from the camera to the track is $d = 30\ m$.From the geometry,we have $x = d 	an 	heta = 30 	an 	heta$.Differentiating both sides with respect to time $t$,we get:$\frac{dx}{dt} = 30 \sec^2 	heta \cdot \frac{d	heta}{dt}$Here,$\frac{dx}{dt} = v_{	ext{car}} = 40\ m/s$ and $\frac{d	heta}{dt} = \omega$ (the angular speed of the camera).So,$40 = 30 \sec^2 	heta \cdot \omega$.At the given position,$	heta = 30^\circ$. Therefore,$\sec 30^\circ = \frac{1}{\cos 30^\circ} = \frac{1}{\sqrt{3}/2} = \frac{2}{\sqrt{3}}$.Thus,$\sec^2 30^\circ = \left(\frac{2}{\sqrt{3}}ight)^2 = \frac{4}{3}$.Substituting these values into the equation:$40 = 30 \cdot \left(\frac{4}{3}ight) \cdot \omega$$40 = 40 \cdot \omega$$\omega = 1\ rad/s$.

Similar Questions

$A$ particle performing $U.C.M.$ of radius $\frac{\pi}{2} \ m$ makes $x$ revolutions in time $t$. Its tangential velocity is

$A$ particle is moving with constant angular acceleration $4 \text{ rad/s}^2$ in a circular path. At what time will the magnitudes of its tangential acceleration and centripetal acceleration be equal (in $\text{ s}$)?

$A$ particle moves along a circle of radius $r$ with constant tangential acceleration. If the velocity of the particle is $v$ at the end of the second revolution after the motion has started,then the tangential acceleration is

$A$ body rotating with an angular speed of $600 \, rpm$ is uniformly accelerated to $1800 \, rpm$ in $10 \, s$. The number of rotations made in the process is ..... .

Identify the increasing order of the angular velocities of the following:
$1$. Earth rotating about its own axis
$2$. Hour hand of a clock
$3$. Second hand of a clock
$4$. Flywheel of radius $2 \ m$ making $300 \ rpm$

Vedclass Test Series

Exam Paper Generator

Online Exam Module