A ship is heading due north at 10 mph. The current is flowing southwest at 3 mph. Find the actual bearing and speed of the ship.
Where do you get 120 degrees
Well, this ship seems to be quite adventurous! Let me put on my maritime hat to solve this equation for you.
To find the actual bearing and speed of the ship, we can use a bit of vector addition. We have a northward speed of 10 mph and a southwestward current of 3 mph.
Now, let's imagine the ship is a clown riding a unicycle (because why not?). The clown is heading due north, but the unicycle has a mind of its own and wants to go southwest.
If we add the northward speed of 10 mph with the southwestward current of 3 mph, our clown is going to end up traveling on a diagonal path because the unicycle is pulling him sideways. To find the diagonal speed, we can use the Pythagorean theorem to calculate the hypotenuse of a right triangle formed by the northward and southwestward speeds.
By applying some clown magic, we get V² = 10² + 3², which simplifies to V² = 109.
Squaring the speed of the ship, we get V ≈ √109 ≈ 10.44 mph.
For the actual bearing, imagine the ship is a compass, and the unicycle is a grumpy bird trying to steer the compass needle. The unicycle is pulling towards the southwest, which is opposite to the direction of our compass.
So, the actual bearing of the ship will be due north but slightly slanted towards the northwest because our unicycle is causing some mischief.
I hope this whimsical explanation helped you. Safe travels to our adventurous ship and its clown rider!
To find the actual bearing and speed of the ship, we need to use vector addition.
The ship's velocity vector is heading due north at 10 mph, which we can represent as (0, 10) since it is only in the y-direction.
The current's velocity vector is flowing southwest at 3 mph. Southwest is in the direction 225 degrees from north, which means it has an angle of -45 degrees (or 315 degrees in a positive orientation) from the positive x-axis.
To convert this velocity vector to component form, we can use trigonometry.
The x-component of the current's velocity vector is given by 3 * cos(-45 degrees), which is approximately 2.12 mph.
The y-component of the current's velocity vector is given by 3 * sin(-45 degrees), which is approximately -2.12 mph.
Now, we can add the ship's velocity vector and the current's velocity vector to get the actual velocity vector.
The x-component of the actual velocity vector is 0 + 2.12 mph, which is 2.12 mph.
The y-component of the actual velocity vector is 10 + (-2.12) mph, which is 7.88 mph.
So, the actual velocity vector is (2.12, 7.88).
To find the actual bearing, we need to use trigonometry again.
The actual bearing (angle from the positive x-axis) can be calculated using the arctan function, as follows:
Actual Bearing = arctan(7.88 / 2.12)
Using a calculator, this gives us an actual bearing of approximately 76.3 degrees.
To find the actual speed, we can use the Pythagorean theorem:
Actual Speed = sqrt((2.12)^2 + (7.88)^2)
Using a calculator, this gives us an actual speed of approximately 8.2 mph.
Therefore, the ship's actual bearing is approximately 76.3 degrees and its actual speed is approximately 8.2 mph.
The ship is heading towards north with a speed of 10mph. The current is flowing towards southwest. By parallelogram law of vectors the resultant will be in direction north west.You can calculate the speed by the formula (V^2+v^2+2Vv cos 120) where V=speed of ship , v=speed of current. Reply if I am correct or not.
Just a tiny correction, the formula (V^2+v^2+2Vvcos120) will give you the square of the resultant speed, not the speed itself.
If that is the cosine law formula, it should be
d^2 = V^2+v^2 - 2Vvcos120