4.)Two points in a plane have polar coordinates (2.80 m, 40.0°) and (4.50 m, 110

Question

4.)Two points in a plane have polar coordinates (2.80 m, 40.0°) and (4.50 m, 110.0°).

(a) Determine the Cartesian coordinates of these points.
(2.80 m, 40.0°)
x = m
y = m
(4.50 m, 110.0°)
x =    m
y =    m

(b) Determine the distance between them.
m=

6.)A roller-coaster car moves 216 ft horizontally and then rises 115 ft at an angle of 33.0° above the horizontal. It next travels 115 ft at an angle of 46.0° downward (below the horizontal). What is its displacement from its starting point? (Assume the initial horizontal motion of the car to be along the +x axis.)

Explanation / Answer

4.

given point A(r,theta) = (2.8, 40 deg)

B(r,theta) = (4.5 , 110 deg)

a. we know that x = rcos(theta) , y= rsin(theta)

for A, x = 2.8cos(40) = 2.1449

y = 2.8sin(40) = 1.7998

for point B

x = 4.5cos(110) = -1.539

y = 4.5sin(110) = 4.2286

b. distance between these points = sqroot((x1 - x2)^2 + (y1 - y2)^2)

d = sqroot((2.1449 + 1.539)^2 + (1.7998 - 4.2286)^2)

d = 4.4125 m

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