as she pick up her riders a bus driver traverses four successive displacements represented by the expression (-6.30 b)i-(4.00 b cos 40)i-(4.00 sin 40)j+(3.00 b cos 50)i-(3.00 b sin 50)j-(5.00 b)j here b represents one city block,a convenient unit of distance of uniform size; i is east; and j is north. the displacements at 40 degree and 50 degree represent travel on roadways in the city that are at these angles to the main east-west and north-south streets.(a)draw a map of the successive displacements(b)what total distance did she travel? (c)compute the magnitude and direction of her total displacements.

add up all your x (east) distances. I assume that they are all in b units and

-(4.00 sin 40)j
is a typo:
- 6.3 - 4(.766) + 3(.643) = -7.44 b east
(or 7.44 b locks west)
Add up your y (north) distances:
- 4(.643) - 3(.766) - 5 = -9.87 b North
(or 9.87 blocks south)

Total distance
6.3+4+4+3+3+5 = 25.3
Total displacement
7.44 west and 9.87 south
magnitude^2 = 7.44^2+ 9.87^2
so
magnitude = 12.4 b
direction
tan angle below -x axis = 9.87/7.44
angle = 53 degrees below -x axis
or
West 53 degrees South
or
217 degrees true on a compass

The distance is 18.3. 6.3+4+3+5

Total distance is 6.3+4+3+5= 18.3 blocks

Magnitude is 12.4b
tan^-1(-9.9/-7.4)= 53 but since it is in third quadrant, add 180 degrees to get a final angle of 233 degrees.

To solve this problem, we will break it down into smaller steps.

Step 1: Draw a map of the successive displacements.
We will start by representing the initial position as the origin (0, 0) on a coordinate plane. Each displacement can then be represented by an arrow pointing in the corresponding direction and with a length proportional to the magnitude of the displacement.

The four successive displacements given are:
-6.30 b, in the -x direction (west)
-4.00 b cos 40, in the -x direction (west)
-4.00 b sin 40, in the -y direction (south)
+3.00 b cos 50, in the +x direction (east)
-3.00 b sin 50, in the -y direction (south)
-5.00 b, in the -y direction (south)

By adding these displacements sequentially, we can determine the final position.

Step 2: Calculate the total distance traveled.
To calculate the total distance, we need to sum the magnitudes of all the displacements. The magnitude of a displacement given in the form of (a, b) can be calculated using the Pythagorean theorem:
Magnitude = sqrt(a^2 + b^2)

We calculate the magnitude for each displacement and sum them up to obtain the total distance traveled.

Step 3: Compute the magnitude and direction of the total displacement.
Once we have determined the final position, we can calculate the magnitude and direction of the total displacement using the Pythagorean theorem and inverse tangent (arctan) function.

Magnitude = sqrt(x^2 + y^2)
Direction = arctan(y / x)

By following these steps, we can answer each part of the question.

(a) Draw a map of the successive displacements.
(b) Calculate the total distance traveled.
(c) Compute the magnitude and direction of the total displacement.