A ship is heading north at 15km/h in a tide moving at 6km/h westward. Determine the magnitude and direction of the resultant velocity of the ship.

I can't answer it because I don't get the formula. And please give me the formula. I need the answer later. I'll wait! Thankyou in advance!

You have 2 vectors: one pointing north and one pointing west.

Vr = -6 + 15i = 16.2km/h[-68.2o] = 16.2km/h[68.2o] N. of W.

To determine the magnitude and direction of the resultant velocity of the ship, you can use vector addition. The formula to find the resultant velocity is a combination of the Pythagorean theorem and trigonometry.

Let's break down the process step-by-step:

1. Draw a diagram: Draw an arrow representing the ship's velocity of 15 km/h in the north direction (upward) and another arrow representing the tide's velocity of 6 km/h in the west direction (leftward). Label the north arrow as "A" and the west arrow as "B".

2. Measure the lengths: Measure the length of arrow A (north direction) and arrow B (west direction) using a ruler or appropriate scale. Let's say the length of arrow A is 15 cm and the length of arrow B is 6 cm.

3. Use the Pythagorean theorem: Apply the Pythagorean theorem to find the magnitude of the resultant velocity. The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the length of arrow A represents the vertical component of the resultant velocity (northward) and the length of arrow B represents the horizontal component of the resultant velocity (westward).

Using Pythagorean theorem: Resultant velocity^2 = (Vertical component)^2 + (Horizontal component)^2

In our example: Resultant velocity^2 = 15^2 + 6^2

4. Calculate the magnitude: Calculate the square root of the resultant velocity^2 (from step 3) to find the magnitude of the resultant velocity.

In our example: Resultant velocity = √(15^2 + 6^2)

5. Determine the direction: Use trigonometry to determine the direction of the resultant velocity. To find the angle between the resulting velocity and the north direction (or any reference direction you prefer), you can use the inverse tangent (arctan) function.

In our example: Direction angle = arctan(Vertical component / Horizontal component) = arctan(15/6)

Now, using a calculator, find the value of arctan(15/6) to get the direction angle.

6. Interpret the results: The magnitude of the resultant velocity will be the value you calculated in step 4, while the direction will be the value you found in step 5. Make sure to include units when interpreting the answer (in this case, km/h).

By following these steps and using the appropriate measurements, you should be able to calculate the magnitude and direction of the resultant velocity for the given problem.