a ship is traveling due east at 10 km/h. what must be the speed of a second ship heading 30 degrees east of north if it is always due north of the first ship?
The answer is 20 k /h.
To determine the speed of the second ship, let's break down the problem into its components.
We have the following information:
- The first ship is traveling due east at a speed of 10 km/h.
- The second ship is always due north of the first ship.
- The second ship is heading 30 degrees east of north.
To find the speed of the second ship, we need to understand the relationship between the speed, direction, and the components of motion. We can use trigonometry to solve this problem.
Let's consider the velocity vectors for both ships. The velocity vector for the first ship is simply 10 km/h towards the east, which we'll label as V1. The velocity vector for the second ship is unknown, but we'll label it as V2.
Since the second ship is heading 30 degrees east of north, we can split the velocity vector V2 into two components:
1. The northward component: V2n
2. The eastward component: V2e
Now, we need to determine the magnitudes of these components.
The northward component, V2n, is the side adjacent to the angle of 30 degrees in a right triangle. To find V2n, we can use the trigonometric function cosine:
cos(30 degrees) = V2n / V2
The eastward component, V2e, is the side opposite to the angle of 30 degrees in a right triangle. To find V2e, we can use the trigonometric function sine:
sin(30 degrees) = V2e / V2
Given that the first ship is moving at a speed of 10 km/h, and the second ship is always due north of the first ship, we know that the magnitude of the northward component, V2n, must be equal to 10 km/h, while the eastward component, V2e, is unknown.
Using the above equations, we can solve for V2:
cos(30 degrees) = 10 km/h / V2
V2 = 10 km/h / cos(30 degrees)
Now, let's compute the value of V2:
V2 = 10 km/h / cos(30 degrees)
≈ 11.55 km/h
Therefore, the speed of the second ship, heading 30 degrees east of north and always due north of the first ship, should be approximately 11.55 km/h.