Question

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.

*Please explain how you got to your answers/ how you found what to add together, etc*

Answer 1

Well, you will have to draw the map
for displacements add x components and y components separately and for distances:
find each and add
move 1
distance = 6.3
displacement east = -6.3 i
displacement north = 0 j

move 2
distance = 4
displacement east = -4 cos 40 = -3.06 i
displacement north= -4 sin 40 = -2.57 j

move 3
distance = 3
displacement east = 3 cos 50 = 1.93 i
displacement north=-3 sin 50 =-2.30 j

move 4
distance = 5
displacement east = 0 i
displacement north=-5 j

then total distance = 6.3+4+3+5

disp east = -6.3-3.06+1.93+0 =
disp North = 0 -2.57 -2.30 -5

tan angle = disp east/disp north
it will be in quadrant 3 (south west) here so that angle is south of west

Answer 2

oh, put all those in units of b, city blocks :)