A lighthouse is .8 miles away from shore. The light rotates 6 times a minute. How fast in MPH is the spot of light moving along the shore when it is .6 miles away?
So I did the problem and I'm not sure but I think I got 1/.6. is that right?
A lighthouse is .8 miles away from shore. The light rotates 6 times a minute. How fast in MPH is the spot of light moving along the shore when it is .6 miles away?
So I did the problem and I'm not sure but I think I got 1/.6. is that right?
Let's let be the perpendicular distance from the lighthouse to the shore (a straight line) and be the distance of the spot of light from the point on the shore intersected by the distance line segment. Let be the angle subtended by the distance line segment and the beam of light. Let . We may then state:
Differentiating with respect to time , we find:
Solving for and using we have:
For this problem, we are given:
Now, plug 'n' chug.