Question

A vector is expressed in polar notation as A⃗ = ( 35.0 N, 37 ∘) Calculate the components of the vector, and enter them (separated by a comma) in the answer box to express the vector in rectangular notation.

Answer 1

Answer:

A = (27.95 N, 21 N)

Explanation:

The polar co-ordinates are given as:

(r,θ) = (35 N, 37°)

Now, to convert this into polar co-ordinates (x, y), we will use following relations:

r² = x² + y²

(35)² = x² + y²

1225 = x² + y²  ----------- equation (1)

and

tan θ = y/x

tan 37° = y/x

y =  0.753 x   ------------------- equation (2)

Substituting this value in equation (1):

1225 = x² + (0.753 x)²

1225 = 1.567 x²

x² = 1225/1.567

x = √781.32

x = 27.95 N

using this value in equation (2)

y = (0.753)(27.95 N)

y = 21 N

Therefore, the vector can be represented in polar co-ordinates as:

A = (27.95 N, 21 N)