Engineering Board Exam Reviewer · Related Rates (Time Rates) · hard
A lighthouse stands 3 km from a straight shoreline, and its beam rotates at 2 revolutions per minute. How fast is the beam moving along the shore at the point on the shore nearest the lighthouse?
- 18.85 km/min
- 12 km/min
- 75.4 km/min
- 37.7 km/min
Answer
D. 37.7 km/min
Solution
Let be the beam's angle from the perpendicular and x the distance along the shore: x=3 . Then dx/dt=3 2 ,d /dt. With d /dt=2(2π)=4π rad/min and =0 ( 2 =1): dx/dt=12π 37.70 km/min.
More Related Rates (Time Rates) questions
- A point moves along the curve y=x2 so that x increases at 3 units per second. How fast is the distance from the origin to the point…
- The length of a rectangle is increasing at 3 cm/s while its width is decreasing at 2 cm/s. At what rate is the area changing when the…
- A ladder 10 ft long leans against a vertical wall. If the bottom slides away from the wall at 2 ft/s, how fast is the top sliding down the…
- A spherical balloon is being inflated at a rate of 100 cm3/s. Find the rate of change of the radius when the radius is 5 cm.
- Water is poured into a conical tank (vertex down) at a rate of 12 m3/min. The tank has a height of 10 m and a top radius of 5 m. Find the…
- A man 6 ft tall walks away from a lamp post 18 ft high at a rate of 5 ft/s. Find the rate at which his shadow is lengthening.
- For the same man and lamp post as above (man 6 ft tall, post 18 ft, walking at 5 ft/s), find the rate at which the tip of his shadow is…
- A boat is pulled toward a dock by a rope passing through a pulley on the dock 8 ft above the water. If the rope is pulled in at 3 ft/s…
- A kite is flying at a constant height of 60 ft and moving horizontally away from the person flying it at 5 ft/s. Find the rate at which…
- A stone dropped into a still pond sends out a circular ripple whose radius increases at 1.5 ft/s. Find the rate at which the enclosed area…