Question

I’m gym class you run 22m horizontal then climb a rope vertically for 4.8m. What is the direction angle of your total displacement, as measured from the horizontal?

Answer 1

Horizontal distance covered is given as

$x = 22 m$

vertical distance climbed by is given as

$y = 4.8 m$

now we need top find the angle made by the displacement vector with respect to horizontal

So here we will say that we can use trigonometry to find out the angle with horizontal

The formula is given as

$tan\theta = \frac{opposite \: side}{adjacent \: side}$

here given that

opposite side = 4.8 m

adjacent side = 22 m

now we can plug in all data in above equation

$tan\theta = \frac{4.8}{22}$

$tan\theta = 0.22$

$\theta = tan^{-1}0.22$

$\theta = 12.3 degree$

so here the displacement will make 12.3 degree angle with horizontal