Final Displacement: 5 Blocks, 53 Degrees E of N - Homework Question Explained

[billybobay]

Homework Statement

What is your final displacement if you walk 3 blocks east, then 4 blocks north?


7 blocks, northeast

5 blocks, 53degrees N of E

5 blocks, 53degrees E of N

1 block, north

Homework Equations

square root of 3^2 + 4^2 = square root of 25 d= 5 blocks

arctan (4/3) = 53 degrees

The Attempt at a Solution

5 blocks. would it be 53 degrees E of N or N of E? and why would it be?

I think it would be 5 blocks E of N because you're walking east then north? could you please explain if that's correct and if it's not then why?

 

[grzz]

53 deg is the angle showing how NORTHERN is the resultant displacement from the EAST direction.
So the direction is given as E 53deg N which is the same as N 37deg E.

 

[billybobay]

53 deg is the angle showing how NORTHERN is the resultant displacement from the EAST direction.
So the direction is given as E 53deg N which is the same as N 37deg E.

so 5 blocks E of N would be correct then?

 

[PeterO]

so 5 blocks E of N would be correct then?

Not really. In the description, 3 blocks East then 4 blocks North, "block" amounts to a unit of length. The question really assumes you are in a neighbourhood with a square road grid.
North and East are of course both directions, so you can't say you are a certain distance in a direction from another direction. Like saying 5 metres left of up ??

It is strange to think that you are 5 blocks away after that journey, but the answer expected will be 5 blocks, in the direction E 53^o N

ACtually just read the OP to see their options:
They are expecting 5 blocks 53 degrees North of East.

 

[Curious3141]

Homework Statement

What is your final displacement if you walk 3 blocks east, then 4 blocks north?


7 blocks, northeast

5 blocks, 53degrees N of E

5 blocks, 53degrees E of N

1 block, north

Homework Equations

square root of 3^2 + 4^2 = square root of 25 d= 5 blocks

arctan (4/3) = 53 degrees

The Attempt at a Solution

5 blocks. would it be 53 degrees E of N or N of E? and why would it be?

I think it would be 5 blocks E of N because you're walking east then north? could you please explain if that's correct and if it's not then why?

Homework Statement

Homework Equations

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

Since this is a multiple-choice question, you can actually solve it without a calculator.

You know the distance traveled is 5 blocks (Pythagoras' Theorem, good to remember and instantly recognise the 3-4-5 right triangle).

That leaves the second and third option.

Because the vertical (North) leg is longer than the horizontal (East) leg, the angle opposite the North leg is greater than the angle opposite the East leg (sketch the triangle if you have difficulty visualising this). Since those two angles add up to 90 degrees, the greater angle has to be more than 45 degrees. Since 53 degrees is the only angle measure common in both options, you go with the one that states 53 deg N of E (this is the angle opposite the North leg).

So it's the second option.

(BTW, for clarity, x degrees N of E means you face due East, then rotate yourself x degrees counterclockwise toward the North. x deg E of N means you face due North, then rotate yourself clockwise x degrees towards East).