A glider lands 18 miles west and 5 miles south from where it took off the result of the trip can be described by the vector (-18,-5) use distancs for magnitude and direction to describe this vector a second way.
I believe its south of west but not sure if 19,16 0r 16,19
19 is the miles and 16 is the angle going south of west
Well, it seems you have quite the vector conundrum there! If we're talking about the distance and direction from the starting point to the landing point, let's unravel this with a touch of humor, shall we?
Imagine the glider taking off from a circus in the West. It flies against the wind, determined to reach its destination. However, as all gliders know, sometimes the wind can be quite the prankster. It pushes the glider a tad South, just to keep things interesting.
So, to describe the vector (-18, -5) in a different way, we can say that the glider traveled approximately 19 miles in a Southwesterly direction. Now, imagine a clown juggling those numbers and you'll remember that it took the glider 19 miles to the South and 18 miles to the West. That's the path this adventurous glider chose!
Remember, though, in the world of vectors, conventionally, we mention the West component first followed by South. So, (-18, -5) is the correct representation.
Happy vector problem-solving, my friend!
To describe the vector (-18, -5) in terms of magnitude and direction, we can use the Pythagorean theorem and trigonometric functions.
First, let's calculate the magnitude of the vector using the formula:
Magnitude = √(x^2 + y^2)
Magnitude = √((-18)^2 + (-5)^2)
Magnitude = √(324 + 25)
Magnitude = √349
Magnitude ≈ 18.68 miles (rounded to two decimal places)
Next, let's determine the direction of the vector. We can use the inverse tangent function (arctan or tan^-1) to find the angle:
Direction (θ) = tan^-1(y / x)
Direction (θ) = tan^-1(-5 / -18)
Direction (θ) = tan^-1(5 / 18)
Direction (θ) ≈ 16.26 degrees (rounded to two decimal places)
To summarize, the vector (-18, -5) can be described as having a magnitude of approximately 18.68 miles and a direction of approximately 16.26 degrees (south of west).
To describe the vector (-18, -5) in terms of magnitude and direction in a second way, you can use the Pythagorean theorem to calculate the magnitude (distance) of the vector.
Magnitude (distance) = √((-18)^2 + (-5)^2)
Magnitude (distance) = √(324 + 25)
Magnitude (distance) = √349
Magnitude (distance) ≈ 18.67 miles
To determine the direction, you can use trigonometry:
Direction = arctan((-5)/(-18))
Direction ≈ arctan(5/18)
Direction ≈ 15.94° (rounded to the nearest hundredth)
Therefore, the vector (-18, -5) can be described as approximately 18.67 miles at an angle of 15.94° south of west.
well, of course it's south and west; they told you that. Where did the 19,16 come from?
distance: √(18^2+5^2) = √349 = 18.68
angle: tanθ = -5/-18, so θ=195.5° = W15.5°S, or a bearing of 254.5°