Finding bearing and position vectors of moving ships

In summary, the question asks for the bearing of a ship S and its position and velocity in relation to a fixed origin O. At noon, S is at a position vector of 8i km and R is at O. At time t hours after noon, the position vectors of S and T are s km and r km respectively. The value of T and the distance between S and R at time T hours are also requested. The bearing of S is found to be 56.3 degrees and s and r are given in terms of t. The value of T is 8, not 2 as originally thought, and the distance between S and R is unknown.
  • #1
phospho
251
0
In this question the unit vectors i and j are due east and north respectively and position vectors are given with respect to a fixed origin O.

A ship S is moving with constant velocity (2i−3j) km h−1 and a ship R is moving with constant velocity 6i km h−1.

a Find the bearing along which S is moving.

At noon S is at the point with position vector 8i km and R is at O. At time t hours after noon, the position vectors of S and T are s km and r km respectively.

b Find s and r, in terms of t.

At time T hours, R is due north-east of S. Find

c the value of T,

d the distance between S and R at time T hours.


I need help with part c)

Answer to a) 56.3, b) s=8i+(2i−3j)t - r=6ti

For part c I'm confused; if R is due south east of S, would it not mean the i and j components would be the same? Well it's wrong and if I do go on to equate the i and j components then I get T = 2, which is incorrect - the right answer is T = 8.

Cheers
 
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  • #2
phospho said:
In this question the unit vectors i and j are due east and north respectively and position vectors are given with respect to a fixed origin O.

A ship S is moving with constant velocity (2i−3j) km h−1 and a ship R is moving with constant velocity 6i km h−1.

a Find the bearing along which S is moving.

At noon S is at the point with position vector 8i km and R is at O. At time t hours after noon, the position vectors of S and T are s km and r km respectively.

b Find s and r, in terms of t.

At time T hours, R is due north-east of S. Find

c the value of T,

d the distance between S and R at time T hours.


I need help with part c)

Answer to a) 56.3, b) s=8i+(2i−3j)t - r=6ti

For part c I'm confused; if R is due south east of S, would it not mean the i and j components would be the same? Well it's wrong and if I do go on to equate the i and j components then I get T = 2, which is incorrect - the right answer is T = 8.

Cheers

R is due north-east of S. The i and j components of what are equal?

ehild
 
  • #3
ehild said:
R is due north-east of S. The i and j components of what are equal?

ehild

S and R I think
 

What is the purpose of finding bearing and position vectors of moving ships?

The purpose of finding bearing and position vectors of moving ships is to accurately determine the location and direction of a ship at any given time. This information is crucial for navigation, tracking, and safety purposes.

How do you calculate the bearing and position vectors of a moving ship?

The bearing and position vectors of a moving ship can be calculated using mathematical formulas that take into account the ship's speed, direction, and time. The most common method is to use vector addition and trigonometry to determine the direction and magnitude of the ship's movement.

What factors can affect the accuracy of the bearing and position vectors?

The accuracy of the bearing and position vectors can be affected by various factors such as the ship's speed and direction changes, environmental conditions (e.g. wind, currents), and errors in measurements or calculations. It is important to regularly update and adjust the vectors to ensure accuracy.

Can the bearing and position vectors be used to determine the destination of a ship?

Yes, the bearing and position vectors can be used to determine the destination of a ship by continuously tracking and updating the vectors. The destination can be estimated by projecting the current movement of the ship onto a map or chart.

How does the accuracy of the bearing and position vectors affect the safety of a ship?

The accuracy of the bearing and position vectors is crucial for the safety of a ship as it allows for precise navigation and avoiding potential hazards such as other ships, shallow waters, or obstacles. Inaccurate vectors can lead to collisions, groundings, or other dangerous situations.

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