A lighthouse sits on a shoreline, rotating its light at a constant rate of 12.0
ID: 2269522 • Letter: A
Question
A lighthouse sits on a shoreline, rotating its light at a constant rate of 12.0 rpm in the direction shown in the over-head view below (drawing is not to scale). A speedboat is moving eastward, parallel to the shore, along the path shown, with a constant acceleration of 3.78 m/s2 (it
A lighthouse sits on a shoreline, rotating its light at a constant rate of 12.0 rpm in the direction shown in the over-head view below (drawing is not to scale). A speedboat is moving eastward, parallel to the shore, along the path shown, with a constant acceleration of 3.78 m/s2 (it's speeding up). At a certain moment, the boat is at point A, directly north of the lighthouse-and the light is shining on it. The next time the light shines on the boat is 4.56 seconds later, and the boat is at point B. Point A is 109 m from the light. How fast was the boat moving at point A?Explanation / Answer
First: look at the diagram. Let's label the position of the lighthouse "C".
Now we ha a right triangle (ABC) and we want ta calculate angle C (near the lighthouse).
Since the light rotates at 12 rpm, it will take 5 sec to make one revolution(360 degrees).
Therefore in 4.56 s, the light rotates 4.56/5 = 0.912 revolutions( this is 328.32 degrees.
Therefore the angle C (inside the right triangle) = 31.68 degree.
The distance AB = (109)(tan31.68) = 67.267 m (this is the distance traveled by the boat in 4.56 s).
The distance formula for the boat: d = (Vo)(t) + (at^2)/2.
Plugging in the numbers we have:
67.267 = (Vo)(4.56) + (3.78)(4.56^2)/2 =>
Answer: V = 6.13 m/s (rounded to three significant digits)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.