Aradar antenna, making one revolution every 5 seconds, is located on a ship that is 6 km from a straight shoreline. how fast is the radar beam moving along the shoreline when the beam makes an angle of 45◦ with the shore?

The figure below is showing the situation:

Figure

Now let the point is at a distance x from the shoreline where it is making the angle of 45 degrees.

So we have:

x

=

6

tan

θ

Now we have:

d

θ

d

t

=

2

π

5

So we have to find the velocity that is given by:

d

x

d

t

=

d

d

θ

(

6

tan

θ

)

=

6

sec

2

(

θ

)

d

θ

d

t

=>

d

x

d

t

=

6

sec

2

(

π

4

)

2

π

5

is the required velocity

Step-by-step explanation:

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step-by-step explanation: