Problem Sheet 4
1.
Two points in the plane have polar coordinates (2.50m, 30.0
°
) and (3.80m, 120.0
°
).
Determine
a.
The Cartesian Coordinates
b.
The distance between them
2.
Two points in the plane have Cartesian coordinates (2.00, -4.00) m and (-3.00, 3.00) m.
Determine
a.
The distance between the points
b.
Their Polar Coordinates
3.
Vector A has a magnitude of 8.00 units and makes an angle of 45
°
with the positive x-
axis. Vector B also has a magnitude of 8.00 units and is directed along the negative x-
axis. Using the graphical methods, find
a.
The vector sum A + B
b.
The vector difference A – B
c.
The unit vector of A in Cartesian Coordinates
d.
The unit vector of B in Cartesian Coordinates
4.
A roller coaster car moves 200 ft horizontally and then rises 135 ft at an angle of 30
°
above the horizontal. It then travels 135 ft at an angle of 40.0
°
downward. What is the
displacement from the starting point?

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