A ship at A is to sail to C, 56km north and 258km east of A. After sailing N25°10’E for 120mi to P, the ship is headed toward C. Find the distance of P from C and the required course to mean C.
duplicate question.
Call the vector from B to C "v2"
Call the vector from the starting point to C "v3".
v3 = 56 j + 258 i
Call the first leg of the voyage, from A to B, "v1"
Perform the vector operation
v2 = v3 - v1
The magnitude and direction of v2 will be your answer.
To find the distance of point P from point C, we can use the distance formula and trigonometry.
Let's break down the given information step by step:
1. The ship is at point A, and it needs to sail to point C, which is 56km north and 258km east of A.
2. After sailing N25°10’E for 120 miles, the ship reaches point P, which is on the way to C.
To find the distance of P from C, we can use the Pythagorean theorem:
Distance(A to C) = sqrt((north distance)^2 + (east distance)^2)
Distance(A to C) = sqrt((56km)^2 + (258km)^2)
Distance(A to C) = sqrt(3136km^2 + 66564km^2)
Distance(A to C) = sqrt(69600km^2)
Distance(A to C) = 264km (approximately)
So, the distance from P to C is 264km.
The required course to mean C can be found using trigonometry. We'll use the concept of angles and sides in a right triangle:
1. The ship sailed N25°10’E for 120 miles to reach P.
This means that, with reference to the north, the angle between the ship's path and the north direction is 25°10'.
2. We can use this information to find the required course to mean C.
The required course is the angle between the ship's path from P and the east direction.
Using trigonometry, we have:
Angle = 90° - angle between the ship's path and the north direction
Angle = 90° - 25°10'
Angle = 90° - (25 + (10/60))°
Angle = 90° - (25.1667°)
Angle = 64.8333° (approximately)
Hence, the required course to mean C is approximately 64.83° east of the north direction.