Posted by **saud** on Sunday, October 30, 2011 at 6:52pm.

A searchlight rotates at a rate of 4 revolutions per minute.?

The beam hits a wall located 13 miles away and produces a dot of light that moves horizontally along the wall. How fast (in miles per hour) is this dot moving when the angle between the beam and the line through the searchlight perpendicular to the wall is pi/6? Note that dtheta/dt=4(2pi)=8pi.

- calculus -
**bobpursley**, Sunday, October 30, 2011 at 7:07pm
velocity= dtheta/dt * distance

in the units you have, with distance in miles, and dt in minutes, velocity will be in miles/minute

- calculus -
**H H Chau**, Friday, August 22, 2014 at 6:46pm
θπ

cos(π/6)=sqrt(3)/2

sec^2(π/6)=4/3

dθ/dt=4 rev/min = 8π rad/min

tan(θ)=x/13

x=13 tan(θ)

dx/dt=13 sec^2(θ) dθ/dt

At θ=π/6

dx/dt=13*(4/3)*8π=435.6 miles/min = 26138 miles/hr

- calculus -
**H H Chau**, Friday, August 22, 2014 at 6:47pm
Note to above attempt: velocity in x-direction, not radial velocity.

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