To find the distance Charles is from his starting point and the course required to return to the marina, we can follow these steps:
a)
1. Calculate the distance traveled in the first leg:
Distance = speed × time
Distance = 18 km/h × 1.5 h = 27 km
2. Find the coordinates of Charles after the first leg:
Since Charles went 10° west of north, this creates a right triangle with a 10° angle.
Using trigonometry, we can find the northward and westward components of his displacement.
Northward displacement = 27 km × sin(10°)
Westward displacement = 27 km × cos(10°)
3. Calculate the total displacement after the first leg using Pythagoras theorem:
Total displacement = √(Northward displacement² + Westward displacement²)
4. Calculate the distance from the marina after the first leg:
Distance = Total displacement
b)
1. Determine the angle between Charles' final position and the marina:
Since Charles is heading 60° east of north after the second leg, the angle he needs to turn to face the marina is 60°.
To return directly to the marina, he would need to turn 60° to the left (port) from his current heading.
2. The course required for Charles to return directly to the marina would be 60° to the left from his current heading, which is 60° east of north.
By following these steps, you can find both the distance from the starting point and the course Charles needs to take to return to the marina.
