Answer:
a) Cartesian coordinates of (2.50 m, 30.0°) = (2.17.1.25)
Cartesian coordinates of (3.80 m, 120.0°) = (-1.90.3.29)
b) Distance between (2.17.1.25) and (-1.90.3.29) = 4.55 meter.
Explanation:
Points in polar coordinates = (2.50 m, 30.0°) and (3.80 m, 120.0°)
(2.50 m, 30.0°) = (2.50*cos 30, 2.50*sin 30) = (2.17.1.25)
(3.80 m, 120.0°) = (3.80*cos 120, 3.80*sin 120) = (-1.90.3.29)
a) Cartesian coordinates of (2.50 m, 30.0°) = (2.17.1.25)
Cartesian coordinates of (3.80 m, 120.0°) = (-1.90.3.29)
b) We have distance between (a,b) and (c,d) by distance formula [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]
So distance between (2.17.1.25) and (-1.90.3.29) = [tex]\sqrt{(-1.9-2.17)^2+(3.29-1.25)^2}=\sqrt{20.7265}=4.55 meter[/tex]
Distance between (2.17.1.25) and (-1.90.3.29) = 4.55 meter.
Answer:
[tex]x_1 = 2.16 m[/tex]
[tex]y_1 = 1.25 m[/tex]
[tex]x_2 = -1.90[/tex]
[tex]y_2 = 3.29 m[/tex]
Part b)
[tex]d = 4.54 m[/tex]
Explanation:
Part a)
Polar coordinates is given as
[tex]r_1 = (2.50 m, 30^o)[/tex]
so we have
[tex]x = r cos\theta[/tex]
[tex]y = r sin\theta[/tex]
[tex]x_1 = 2.50 cos30 = 2.16 m[/tex]
[tex]y_1 = 2.50 sin30 = 1.25 m[/tex]
similarly we have
[tex]r_2 = (3.80, 120 ^o)[/tex]
[tex]x_2 = 3.80 cos120 = -1.90[/tex]
[tex]y_2 = 3.80 sin120 = 3.29 m[/tex]
Part b)
now the distance between two coordinates
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]d = \sqrt{(-1.90 - 2.16)^2 + (3.29 - 1.25)^2}[/tex]
[tex]d = 4.54 m[/tex]
