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Question

A racing car is travelling along a track at a constant speed of 40 m/s
A T.V. camera men is recording the event from a distance of 30 m directly away from the track as shown in figure. In order to keep the car under view in the position shown, the angular speed with which the camera should be rotated, is


A
43 rad/sec
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B
833 rad/sec
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C
34 rad/sec
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D
1 rad/sec
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Solution

The correct option is D 1 rad/sec

Step 1:Draw a rough diagram of given problem

x is the distance travelled by car at any time t

Step 2: Find angular speed of car.
Formula Used: dθdt=ω
From figure
tanθ=x30
LHS=ddt(tanθ)
=ddθ(tanθ).dθdt=sec2θ.ω

Asdθdt=ω
Step 3: Find angular speed of car.
RHS=ddt(x30)=4030
Asdxdt=v=30 m/s
sec2 θ.ω=4030
θ=30and sec230=23
we get43.ω=4030
ω=1 rad/s
Final Answer: (d)




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