Question

a ship departed from the port in a north-easterly direction towards a bove B in the sea then it sails at a rate of 298 degrees towards a lighthouse L which is located north of port P. Find the routes at which the ship should sail

Answer 1

The problem requires an understanding of vector addition and subtraction to find the correct routes a ship should sail based on angles and directions. Vector mathematics is utilized to determine the ship's course when affected by currents or when following specific navigational directions.

Step-by-step explanation:

The question involves vector addition and subtraction to determine the route a ship should sail based on given angles and directions. When considering the problem of a ship departing a port in a north-easterly direction and then sailing at 298 degrees towards a lighthouse north of the port, or a woman sailing a boat with specific directional instructions, we use vector mathematics to solve the navigation issues. For example, the woman sailing a boat must first sail 27.5 m at 66.0° north of east and then travel 30.0 m at 112° north of east. If she travels in the opposite direction for the second leg, vector subtraction will be used to find her new location.

In the case of a ship affected by a local ocean current while trying to maintain a certain course, such as the ship in Rotterdam sailing due north with an ocean current coming from the north-east, vector addition is required to establish the ship's velocity relative to Earth.

Answer 2

The ship's new route towards the lighthouse L is at a bearing of 343 degrees measured clockwise from north.

The problem describes the ship's departure from a port in a north-easterly direction towards point B in the sea and then sailing at a rate of 298 degrees towards a lighthouse L, which is located north of the port P. Let's break down the information:

Departure from Port to Point B:

The ship departs in a north-easterly direction. This means it is initially heading somewhere between north (0 degrees) and east (90 degrees).

The bearing is not specified, so let's assume it's heading due north-east, i.e., at a bearing of 45 degrees.

Sailing towards Lighthouse L:

The ship then changes its course to 298 degrees towards the lighthouse.

The bearing of 298 degrees is measured clockwise from north.

Initial Route (Port to B): The ship departs at a bearing of 45 degrees.

Change in Route (B to Lighthouse L): The ship changes its course to 298 degrees. To find the new route, add 298 degrees to the initial bearing of 45 degrees.

New Route=Initial Bearing + Change in Course

New Route=45∘ +298∘

New Route=343∘

the ship's new route towards the lighthouse L is at a bearing of 343 degrees measured clockwise from north.