Question

A ship A steaming due north at 10 km per hour sights at noon, a second ship B in direction due east and 12 km away steaming northeast at 5 km per hour. Calculate, to the nearest degree, the bearing of A from B at 12:15 pm?

A. 37°

B. 53°

C. 127°

D. 143°

Answer 1

To find the bearing of ship A from ship B at 12:15 pm, subtract the displacement of ship A from the displacement of ship B and measure the angle of the resulting displacement from the north direction. The bearing of A from B is approximately 53° to the nearest degree.

Step-by-step explanation:

To find the bearing of ship A from ship B at 12:15 pm, we need to determine the direction of ship B relative to ship A. Let's break down the problem step by step:

1. At 12:00 pm, ship A is steaming due north at 10 km/h.
2. At the same time, ship B is 12 km away and steaming northeast at 5 km/h.
3. In 15 minutes (from 12:00 pm to 12:15 pm), ship A will move 2.5 km (10 km/h * 0.25 h).
4. Now, the relative position of ship B from ship A can be found by subtracting the displacement of ship A from the displacement of ship B. In this case, the displacement of ship B is 12 km northeast, and the displacement of ship A is 2.5 km due north.
5. Using graphical vector addition or trigonometry, we can find that the resulting displacement of ship B from ship A is approximately 10.5 km north-northeast.
6. The bearing of A from B can be found by measuring the angle between the resulting displacement and the north direction. In this case, the bearing of A from B is approximately 53° to the nearest degree.