Question

A ship at position (1, 0) on a nautical chart (with north in the positive y direction) sights a rock at position (6, 5). What is the vector joining the ship to the rock? (This is called the bearing of the rock from the ship. Round your answer to two decimal places.) answer should be in radians east of north

Answer 1

The vector joining the ship to the rock is t= 7 i + 5 j

The direction is 0.9505 radians east of north.

Explanation:

The position vector of the ship:

r= 1 i + 0 j

The position vector of the ship:

s= 6 i + 5 j

The vector joining the ship to the rock is:

t = r + s

t = (1 i + 0 j) + (6 i + 5 j)

t = 7 i + 5 j

The bearing of the rock to the ship is:

Θ=
`( \pi)/(2) - arctan ((5)/(7))`= 0.9505 radians