A small boat is headed for a harbor 34 km directly northwest of its current posi
ID: 2128373 • Letter: A
Question
A small boat is headed for a harbor 34 km directly northwest of its current position when it is suddenly engulfed in heavy fog. The captain maintains a compass bearing of northwest and a speed of 10.5 km/h relative to the water. The fog lifts 3.0 h later and the captain notes that he is now exactly 4.5 km south of the harbor. (a) What was the average speed of the current during those 3.0 h?1 km/h
(b) In what direction should the boat have been heading to reach its destination along a straight course?
2 (a) What was the average speed of the current during those 3.0 h?
1 km/h
(b) In what direction should the boat have been heading to reach its destination along a straight course?
2
Explanation / Answer
1. v_boat w.r.t ground = sqrt(34^2 + 4.5^2) / 3 = 11.43 km/h
speed of current = sqrt ( 11.43^2 - 10.5^2) = 4.52 km/h
2. 10.5cos(theta) = 4.52
theta = cos-1(4.52/10.5) = 64.50 degrees.
3. den boat will have only speed of 10.5sin64.50 = 9.48 km/h
t = 34/9.48 = 3.59 hr