Suppose you first walk a 100 m in a direction 1 21 west of...

Suppose you first walk A = 10.0 m in a direction θ1 = 21° west of north and then B = 21.4 m in a direction θ2 = 45.0° 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 the figure below, then this problem finds their sum R = A + B. Give the direction in degrees south of west.) distance - m direction - ° south of west

Transcript

00:01 In this question it is given that you are walking a distance of a is equal to 10 meters in a north of west direction.

00:12 A is equal to 10 meters in a north of west direction.

00:22 And a distance of p is equal to 21 .4 meters in a south of west direction.

00:32 We need to determine the distance between the starting point and the end point.

00:40 Also we need to determine the direction.

00:43 Now let us consider this is east direction and this one is west direction and this is south and this one is north.

00:57 Let us consider this is the vector a for the magnitude of 10 meters and this is the vector b for the magnitude of 10 meters and this is the vector b for the magnitude of 21 .4 meters.

01:12 Now you are walking from this point this is the origin 4.

01:18 So starting from this point you are walking this direction after that you are walking this direction.

01:24 So this is making an inclination of 21 degrees this is making an inclination of 21 degrees and this one is making an inclination of 45 degrees.

01:47 Now we know that this vector a, this vector a will have two components, one will be the horizontal component, another one will be the vertical component.

01:56 Let us say this is our x -axis and this is our y -axis and the horizontal component will be acting in this direction and vertical component will be acting in the vertically upward direction.

02:09 Similarly the vector b will have two components, one will be the horizontal component will be acting towards left and the vertical component will be acting in the vertically downward direction.

02:22 Now let us write on the component.

02:26 Let us say, ax is the horizontal component of the vector a.

02:33 This is equal to 10 cost 21 degrees.

02:41 On calculation we obtained this is final 9 .34...

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