Question

1.An airplane is 320 km and 35^o north of west from the airport. What is the position of the airplane in polar coordinate?

2.What is the vector A = (2.5, 120^o) in Cartesian coordinate?

3.What is A = (- 1.5, - 3.2) in polar coordinate?

4.What is C = A + B if A = (1.2, 3.0^o) and B = (2.0, 160^o)?

5.What is C = 0.23A if A = (2.6, 45^o)?

6.What is B = 1.2A if A = (2.0, 3.0)?

Answer 1

To convert from Cartesian Coordinates (x,y) to Polar Coordinates (r,θ):

1. r = √ ( x² + y² )
2. θ = tan^-1 ( y / x )

2)
120 = arctan( y / x )
2.5= sqrt( x2 + y2 )
x^2 + y^2 = sqrt(2.5)
x = sqrt (sqrt(2.5) - y^2)

120 = arctan( y / sqrt (sqrt(2.5) - y^2) )

so, y = -1.089

and x = sqrt (sqrt(2.5) - (-1.089 )^2) = 0.628

(x,y) = (0.628,-1.089)

Solve 1 similarly

3) r = √ ( x² + y² )

θ = tan^-1 ( y / x )

4) Convert to rectangular coordinates then add/subtract. Convert back to polar coordinates.

5).What is C = 0.23A if A = (2.6, 45o)?
C = (0.23 * 2.6 , 45o)

6).What is B = 1.2A if A = (2.0, 3.0)?
B = (1.2 * 2.0,1.2* 3.0 )