Question

. 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.

Answer 1

Answer:

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