Solution Found!
Suppose you first walk 12.0 m in a direction 20º west of
Chapter 3, Problem 5(choose chapter or problem)
Suppose you first walk 12.0 m in a direction \(20^{\circ}\) west of north and then 20.0 m in a direction \(40^{\circ}\) south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements \(A\) and \(B\) , as in Figure 3.56, then this problem finds their sum \(R=A+B\).)
Questions & Answers
QUESTION:
Suppose you first walk 12.0 m in a direction \(20^{\circ}\) west of north and then 20.0 m in a direction \(40^{\circ}\) south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements \(A\) and \(B\) , as in Figure 3.56, then this problem finds their sum \(R=A+B\).)
Step 1 of 4
The diagram is given as,
Step 2 of 4
From the given diagram, the component of vector A along the x-direction is,
\({A_x} = - A\sin \theta \)
Here \(\theta\) is the angle from the positive x-axis in the anti-clockwise direction.
Substitute the values in the above expression, and we get,
\({A_x} = - 12\sin 20^\circ \)
\({A_x} = - 4.1\;{\rm{m}}\)
The component of vector A along the y-direction is,
\({A_y} = A\cos \theta \)
Substitute t