A ship sails north at 15 km/h but drifts westward with the tide at 8 km/h. What is the resultant velocity of the ship?

Help me Please

draw a diagram of the velocities.

Recognize an 8-15-17 right triangle?

That is a right triangle:

speed=sqrt(15^2+8^2)
direction: arctan(8/15) W of N

That is a strong tide.

To find the resultant velocity of the ship, we need to use vector addition. The magnitude of the resultant velocity can be calculated using the Pythagorean theorem, and the direction can be determined using trigonometry.

Let's consider the northward velocity as the y-component of the velocity vector and the westward velocity as the x-component of the velocity vector.

Given:
Northward velocity (Vn) = 15 km/h
Westward velocity (Vw) = 8 km/h

We can find the magnitude of the resultant velocity (Vr) using the Pythagorean theorem:
Vr = √(Vn^2 + Vw^2)
= √(15^2 + 8^2)
= √(225 + 64)
= √289
= 17 km/h

So, the magnitude of the resultant velocity is 17 km/h.

To find the direction, we can use the inverse tangent function:
θ = tan^(-1)(Vn/Vw)
θ = tan^(-1)(15/8)
θ ≈ 61.93 degrees

The direction of the resultant velocity is approximately 61.93 degrees north of west.

Therefore, the resultant velocity of the ship is approximately 17 km/h, 61.93 degrees north of west.

To find the resultant velocity of the ship, we need to use vector addition since the ship is moving in two different directions.

The ship's velocity can be broken down into two components: one traveling north and one traveling west.

The northward velocity is 15 km/h, while the westward velocity is 8 km/h.

To find the resultant velocity, we'll use the Pythagorean theorem:

Resultant velocity = √(northward velocity^2 + westward velocity^2)

Plugging in the values:

Resultant velocity = √(15^2 + 8^2)
= √(225 + 64)
= √289
= 17 km/h

Therefore, the resultant velocity of the ship is 17 km/h.