Question

A beacon makes one revolution every 10 seconds. It is located on a ship w
from a straight shore line. How fast is the beam moving along the shore
angle of 45° with the shore?​

Answer 1

Answer:

Step-by-step explanation:

Given  A beacon makes one revolution every 10 seconds. It is located on a ship 2 km from a straight shore line. How fast is the beam moving along the shore  angle of 45° with the shore?

The rate of π / 5 radians / sec is equal to one revolution every 10 secs.

It can be written as dθ / dt = π / 5

Also x = 2000 tan θ and dx / dθ = 2000 sec^2 θ

We know that dx/dt = dx/dθ x dθ / dt

                              = 2000 sec^2 θ x π / 5

                                 = 400 π sec^2 θ

Now angle with shoreline is 45 degree, θ = π / 4

So dx / dt = 400 π sec^2 π / 4

               = 800 π m / s

So the beam is moving along the shoreline at a speed of 800 π m / s