How fast (km/h) is the dot moving when θ= π/5?

Question

A laser pointer is placed on a platform that rotates at a rate of 5 revolutions per minute. The beam hits a wall 8km away, producing a dot of light that moves horizontally along the wall. Let θ be the angle between the beam and the line through the lines through the searchlight perpendicular to the wall. How fast (km/h) is the dot moving

when θ= π/5?

Note: dθ/dt = 5(2π) = 10π.

Answer 1

if the dot is traveling 5 revolutions/min. That means that it is traveling 5*2pi radians/minute (angular velocity)

The dot is 8 km away which means that the radius is 8 km.

The velocity of the dot is r x w where r is the radius and w is the angular velocity.

So, v = r x w = 8 x 10pi = 80pi km/minute