A vessel sails 32 miles S 45 degrees E. How far south has it sailed?
The wording of it confuses me.
Total distance travelled is 32 miles. The south component of the displacement is is 32 cos 45 = 22.63 miles. On a map, that is how much the southern coordinate changes.
There is an eastern displacement of the same amount, 32 sin 45 = 22.63 miles.
The hypotenuse, which is the displacement vector magnitude, is 45 miles
The hypotenuse, which is the displacement vector magnitude, is 32 miles
To calculate how far south the vessel has sailed, we need to break down the given information.
The vessel sailed 32 miles in a direction of S 45 degrees E.
"S" stands for south, and "45 degrees E" means the vessel is deviating 45 degrees eastward from the south direction.
To determine how far south the vessel has sailed, we need to find the south component of the displacement.
We can use trigonometry to calculate it using the given angular deviation. The south component can be found using the formula:
South component = Total distance * sine of angle
In this case, the total distance sailed is 32 miles, and the angle is 45 degrees. Let's substitute these values into the formula:
South component = 32 miles * sine(45 degrees)
To calculate this, you can use a scientific calculator or an online calculator. Taking the sine of 45 degrees gives us approximately 0.7071.
South component ≈ 32 miles * 0.7071
South component ≈ 22.63 miles
Therefore, the vessel has sailed approximately 22.63 miles south.