Answer to Question #88685 in Mechanics | Relativity for Salim ghali salis

Question

While following a treasure map,you start at an old oak tree,you first walk 825m directly south,then turn and walk 1.25km at 30.0degree west north,and finallay walk 1.00km at 40degree north of east,where you find the treasure:a biography of isaac newton.
(a)to return to the old oak tree,in what direction should you head and how far will you walk?use the components to solve this problem.
(b)to see whether your calculationin part (a) is reasonable,check it with a graphical solution drawn roughly to scale.

Answer 1

a) To determine where we are we can simply find components of the final displacement. To do this, put the oak tree - the starting point - to the origin with coordinates (0;0).

To S:

$x = 0;\space y = -825 \text{ m}.$

To WN:

$x = -1250\cdot\text{sin}30^\circ=-652\text{ m};$

$y = -825+1250\text{cos}30^\circ=257.5 \text{ m}.$

To NE:

$x = -652+1000\text{cos}40^\circ=141\text{ m};$

$y =257.5+1000\text{sin}40^\circ=900.3 \text{ m}.$

So we are this far from the tree:

$$f=\sqrt{x_f^2+y_f^2}=\sqrt{141^2+900.3^2}=911.3\text{ m}$$

at this angle:

$$\theta=\text{tan}^{-1}\Big(x_f/y_f\Big)=\text{tan}^{-1}\Big(141/900.3\Big)=8.9^\circ$$

West of South.

b)