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choli [55]
2 years ago
11

a student walks 8 steps east 6 steps northeast 9 steps north west what is her displacement? include magnitude and direction

Mathematics
1 answer:
kati45 [8]2 years ago
8 0

The displacement is 18.03 steps, and the direction is 47.25°

<h3>How to get the displacement?</h3>

We know that displacement is the difference between the final position and the initial position.

We assume the initial position (0, 0). Let's define the positive x-axis as the east and the positive y-axis as the north.

First, the student moves 8 steps east, so she is at:

(0 + 8, 0)

Then she moves 6 steps northeast, so the new position is:

(6*cos(45°) + 8,  6*cos(45°))

Finally, she moves 9 steps due north, so we have:

(6*cos(45°) + 8,  6*cos(45°) + 9)

Then the final position is:

(12.24, 13.24)

So the displacement is:

D = (12.24, 13.24) - (0, 0) =  (12.24, 13.24)

The magnitude of the displacement is:

|D| = \sqrt{12.24^2 + 13.24^2} = 18.03

So the magnitude is 18.03 steps.

And the direction is given by the arctangent of the quotient between the y-component and the x-component:

\theta = Arctg(13.24/12.24) = 47.25 \°

If you want to learn more about displacements:

brainly.com/question/4931057

#SPJ1

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Step-by-step explanation:

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the length of a rectangular garden is 3 m greater than the width. The area of the garden is 70m squared. find the dimensions of
Lerok [7]
A = l x w

so you know that the length is 3m longer than the width, so you could use a formula to represent that

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you then substitute the second equation into the first to solve for l

70 = l x (l +3)
70 = l^2 + 3l

you could then rearrange the formula and solve for l using the quadratic formula 

0 = l^2 + 3l - 70

l = -3 +- (square root (3)^2 - 4(1)(70)) / 2(1)
l = -3 +- (square root 9 + 280) / 2
l = -3 +- (square root 289) / 2
l = -3 +- 17 / 2

then you solve for the two seperate roots

l = -3 + 17 /2
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l = 7

or 

l = -3 - 17 / 2
l = -20 / 2
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since a length cannot be negative, this root is not viable. therefore l = 7

to solve for w you would use

w = l + 3
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hope this helps! if you did not understand a step or concept please let me know!
4 0
3 years ago
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