What is the resultant displacement when a ship sail 200km north and then 150km west
150^2 + 200^2 = c^2
62,500 = c^2
displacement is 250
That is distance (scalar) not displacement (vector)
angle west of north = A
tan A = 15/20 = 3/4 = .75
A = 36.9 deg west of north
or
360 - 36.9 = 323.1 degrees true
To find the resultant displacement of the ship, we can use the Pythagorean theorem.
Step 1: Plot the distances on a graph.
Draw a straight line to represent the 200 km northward movement and another line to represent the 150 km westward movement. You can choose a scale for the axes to make the drawing more convenient.
Step 2: Calculate the distances traveled along the axes.
Given that the ship traveled 200 km north and 150 km west, you have a right-angled triangle. The 200 km northward movement represents the vertical side (y-axis), and the 150 km westward movement represents the horizontal side (x-axis).
Step 3: Apply the Pythagorean theorem.
The Pythagorean theorem states that in any right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse represents the resultant displacement, and the other two sides are the distances traveled along the x-axis and y-axis.
Using the Pythagorean theorem, we can calculate the resultant displacement as follows:
Resultant displacement = √((200 km)^2 + (150 km)^2)
Resultant displacement = √(40000 km^2 + 22500 km^2)
Resultant displacement = √(62500 km^2)
Resultant displacement ≈ 250 km.
Therefore, the resultant displacement of the ship is approximately 250 km.