A pilot flies in a straight path for 1 h 30 min She then mak

A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 12 degree to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 675 mi/h, how far is she from her starting position? mi Two boats leave the same port at the same time. One travels at a speed of 33 mi/h in the direction N 50 degree E, and the other travels at a speed of 24 mi/h in a direction S 70 degree E (see the figure). How far apart are the two boats after 1 h? mi

Solution

Solution:

To determine each distance, use the following equation.

Distance travelled in 1h 30 min (or 1.5 hours)
d = velocity × time = 675mi/h × 1.5h
= 1012.50mi

Distance travelled in next 2 hours
d = velocity × time = 675mi/h × 2h
= 1350mi

We need determine the component that is parallel and the component that is perpendicular to the original direction.

Parallel = 1350 * cos 12 1320.50 miles
Perpendicular = 1350 * sin 12 281 miles
Total parallel = 1012.50 + 1350 * cos 12 2333 miles

To determine the distance from its initial position to its final position, use the Pythagorean Theorem.

d = (x^2 + y^2)
d = [(1012.50 + 1350 * cos 12)^2 + (1350 * sin 12)^2]
d = 2350 mile