Question

Two boats leave a dock together . Each travels in a straight line . The angle between their courses measures 54° 10¢ . One boat travels 36.2 km/hr and the other travels 45.6 km/hr. How far apart will they be after three hours

Answer 1

Answer:

218.93 km

Explanation:

$\theta$ = Angle between the paths of the two boats = 54.10°

Distance = Speed × Time

Distance traveled by one boat = $36.2\times 3\ km$

Distance traveled by other boat = $45.6\times 3\ km$

From the triangle law of vectors we have

$d=\sqrt{(36.2\times 3)^2+(45.6\times 3)^2+2\times 36.2\times 3\times 45.6\times 3\times cos54.10}\\\Rightarrow d=218.93\ km$

The distance they will be apart after 3 hours is 218.93 km