and then walks due east 15.5 km
Magnitude = ? km
Direction = ? degree of north of east
Magnitude = ? km
Direction = ? degree of north of east
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the east component of the first segment = 32.5 cos 45 = 23km
the north component of the first segment = 32.5 sin 45 = 23km
the total east component = 38km
the total north component = 23 km
magnitude of displacement = Sqrt[38^2+23^2] = 44.4km
the angle of the displacement is given by tan(theta) = 23/38
theta = 31.2 deg north of east
the north component of the first segment = 32.5 sin 45 = 23km
the total east component = 38km
the total north component = 23 km
magnitude of displacement = Sqrt[38^2+23^2] = 44.4km
the angle of the displacement is given by tan(theta) = 23/38
theta = 31.2 deg north of east
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This is going to be very hard to describe without a diagram, but I'll do my best!
First thing you need to know is that you need to add the vectors together.
Break the first movement up into two directions.
If you use the Pythagorean Theorem, you find that he walked 23 km north and 23 km east.
Add that to the second movement, during which he walks 0 km north and 15.5 km east.
So overall, he walked (23+15.5)=38.5km east and 23 km north.
Which means you get to set up another triangle and use good ol' Pythagoras to help you get the job done!
In short, you find that his displacement is 44.85 km.
So now to find the angle. Hopefully you know about sin, cos, and tan. Imagine a triangle on a map with north, south, east and west to help you figure it out. Some simple trigonometric functions later we find that he walked 44.85 km 59.15 east of north.
First thing you need to know is that you need to add the vectors together.
Break the first movement up into two directions.
If you use the Pythagorean Theorem, you find that he walked 23 km north and 23 km east.
Add that to the second movement, during which he walks 0 km north and 15.5 km east.
So overall, he walked (23+15.5)=38.5km east and 23 km north.
Which means you get to set up another triangle and use good ol' Pythagoras to help you get the job done!
In short, you find that his displacement is 44.85 km.
So now to find the angle. Hopefully you know about sin, cos, and tan. Imagine a triangle on a map with north, south, east and west to help you figure it out. Some simple trigonometric functions later we find that he walked 44.85 km 59.15 east of north.
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Aah, vectors, my favorite hassle.
First off, you must understand what you are trying to solve for. Remember the Pythagorean theorem? Where A^2 + B^2 = C^2? Well, magnitude/displacement is the the variable C you are solving for. That means that A and B will be the X and Y displacement, respectively. Therefore, C = the hypotenuse, and that's what magnitude is.
When an angle is "north of east" or whatever nonsense they tell you, you essentially have to travel in whichever direction they give you first (east is positive X on an X-Y graph). Then you move the second direction (north is positive Y). It's kinda hard to explain, but luckily you have 45°, so it doesn't matter which one is first as long as you know which quadrant you're solving for.
First off, you must understand what you are trying to solve for. Remember the Pythagorean theorem? Where A^2 + B^2 = C^2? Well, magnitude/displacement is the the variable C you are solving for. That means that A and B will be the X and Y displacement, respectively. Therefore, C = the hypotenuse, and that's what magnitude is.
When an angle is "north of east" or whatever nonsense they tell you, you essentially have to travel in whichever direction they give you first (east is positive X on an X-Y graph). Then you move the second direction (north is positive Y). It's kinda hard to explain, but luckily you have 45°, so it doesn't matter which one is first as long as you know which quadrant you're solving for.
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keywords: and,deg,of,magnitude,if,man,km,east,north,direction,32.5,displacement,45,Determine,walks,the,Determine the magnitude and direction of the displacement if a man walks 32.5 km 45° north of east,