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### Course: Precalculus>Unit 6

Lesson 9: Vectors word problems

# Vector word problem: hiking

Sal solves a word problem with vectors where he finds the total straight-line distance traveled over a few days. Created by Sal Khan.

## Want to join the conversation?

• What if they ask to convert the angle, which is 52 degrees, to radians? What would be the answer then? How do I change from degrees to radians?
• While the math in Yamanqui's answer is correct, I'd like to suggest a slightly different approach that I have found helps students who have trouble grasping the degrees vs. radians concepts:

First, whether in degrees or radians, find out what fraction of a circle the angle you have sweeps out. You do the by dividing that angle by a full angle (360° or 2π radians).

Now you just have the fraction of a circle the angle sweeps out, no degrees nor radians. So, to get degrees or radians, you just multiply by 2π or 360° depending on whether you want radians or degrees.

So, for 52°:
52/360 = 13/90 of a circle
We want radians, so we multiply that fraction by 2π
13/90 × 2π = 13π/45

For going from radians, let us take the angle ³⁄₂π
³⁄₂π ÷ 2π = ¾ of a circle
¾ × 360° = 270°
• Why is his direction at the end of day three not the direction of the vector d3 and instead he calculates it as the direction of the vector dt?
• Because the question is about the angle from the initial camp, not where he started out on the third day. The vector from the initial camp (dt) is the sum of the three “day” vectors.
• Is "__m/s in a certain direction" considered a vector, or not?
• Yes it is. Vectors always have a magnitude (the "__ m/s") and a direction ("in a certain direction"). If the direction is missing then it'd be a scalar not a vector.
Hope this helped:)
• The answer for the total distance on the calculator was 24.28... He tells us that the questions asks for the distance rounded to the nearest tenth place, and reports the answer as 24.2. Shouldn't it be rounded to 23.3?
• The answer on his calculator was the same as that on all of ours: 24.2074368...
What you see as 24.28.. is a digital-style zero with a slash through it
So, when he had to round it, he started with 24.2074368...
He has to round to the tenth place:
24.`2`074368...
so, he checks the next digit after the tenths' place and it is a zero
So it rounds to 24.2
• In the practice question pool, there are a few questions that give a vehicle's initial velocity, but then gives a different velocity when affected by wind, and asks for the magnitude and direction of the wind itself. How do I approach those problems?
• The resultant velocity of the vehicle is equal to the vehicle's initial velocity vector plus the velocity vector of the wind. You just need to set up a vector equation.
• Hi, what if I am only given the length of each distance and the degree of the angle? How would I solve for North and East in that case? For example, if the question said Keita traveled 15km [N 51degrees E] (say, in this case that the Hypotenuse equals 15km); and then gave the hypotenuse length and the angles of all the other distances; how would I get the total displacement?
• Why was 19/15 the inverse tangent? Can somebody please explain the concept of inverse trigonometric functions.
• trigonometric functions are like all other functions in having an inverse.....
If f(x)=y, then the inverse of function f-1(y)=x, in this case....
tan(theta)=19/15 therefore the inverse tan of 19/15 or tan-1(19/15)=theta
The inverse of a function is basically a function that when inputted with the answer of the original function produces an answer which is equal to the input of the original function. For example, if c(x) was the inverse of f(x) and if f(2)=7 then c(7) = 2
• I can't understand the sentence that the 'conventional tangent gives the angle between -pi over 2 and pi over 2'. Could anyone explain this sentence. Thanks in advance.
(1 vote)
• In order to keep the inverse tangent a function (every input corresponds to only 1 output), we have to restrict its domain somehow. The normal tangent graph repeats itself forever and has multiple points that give the same output for different inputs. So when we take the inverse, there would be multiple outputs for one input unless we restrict the domain. A domain interval of 180 degrees captures every possible tangent value. I'm not sure if there's a mathematical reason why arctangent is restricted to -pi/2 and pi/2, besides the fact that this makes it centered at 0 and look nice.
Because the domain is restricted like this, if we want to compute the arctangent of something with a calculator, it will only give us an answer between -pi/2 and pi/2 radians. If you know that the angle in question is in the 2nd or 3rd quadrants, you'd have to account for that yourself when finding the angle by adding 180 degrees to the value you get from the calculator.