Physics, 20.10.2020 16:01 Confusedandlazy

. Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point? What is your displacement vector? What is the direction of your displacement? Assume the +x-axis is to the east.

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The distance from the starting point is 43 m, the displacement vector is 30.81 m and the direction of the displacement is 119.7 degrees.

Given-

Distance travel through the west is 18 m.

Distance travel through the north is 25 m.

Distance from starting point-

To know the total distance, add both the covered distance. Thus total distance x is,

x=18+25

x=43

Hence, the distance from the starting point is 43 m.

The displacement vector-

Displacement is calculated as the shortest distance between starting and final point. This shortest distance can be calculated using the Pythagoras theorem which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore,

d^2=18^2+25^2

d^2=324+625

d^2=949

$d=\sqrt{949}$

d=30.81

The displacement vector is 30.81 m.

The Direction of displacement-

The direction of displacement $\theta$ with these two sides can be calculated with the formula,

$\theta=tan^{-1}\dfrac{25}{-18}$

Here due to the west direction(opposite side), the sign is taken negatively.

$\theta=tan^{-1}(-1.389)$

$\theta=-60.27^o$

For the other quarter,

$\theta=180-60.27=119.7^o$

Hence, the distance from the starting point is 43 m, the displacement vector is 30.81 m and the direction of the displacement is 119.7 degrees.

For more about the displacement, follow the link below-

link

Answer from: helpplz5725

Explanation:

The total distance is how far you walk from the starting point.

Distance through west = 18.0m

Distance through north = 25.0m

Total distance covered = 18.0+25.0m

Total distance covered = 43.0m

This means that I am 43.0m from the starting point

Displacement is the distance covered in a specified direction. The displacement will be gotten using the Pythagoras theorem as shown:

$d^2 = 25^2 + 18^2\\d^2 = 625+324\\d^2 = 949\\d = \sqrt{949}\\ d = 30.81m$

The direction of your displacement is 30.81m

Direction is gotten according to the formula;

$\theta = tan ^{-1}{\frac{y}{x} }\\\theta = tan ^{-1}{\frac{25}{-18} }\\\theta = tan ^{-1}-1.3889}\\\theta = -60.27^0\\\theta = 180-60.27\\\theta = 119.7^0$

Note that the direction to the west is negative, that is why the x is -18.0m

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