Question

A position vector is given to a student in polar form. he is required to convert this position vector to cartesian form (ai bj). assist this student with determining 'b' (the vertical component of the position vector) oa→ = (2.4,44.2

Answer 1

To find the vertical component 'b' from a polar position vector (2.4, 44.2°), use the equation b = r sin(θ), which gives an approximate result of b = 1.67.

Step-by-step explanation:

To determine the vertical component 'b' in Cartesian form from a position vector given in polar form, such as ο→ = (2.4,44.2°), one would use the sine function since the vertical component corresponds to the y-axis. The conversion from polar to Cartesian coordinates involves this general equation for the y-component (or vertical component):

b = r sin(θ)

Given the magnitude of the position vector (r) is 2.4 and the angle (θ) is 44.2 degrees, we calculate:

b = 2.4 sin(44.2°)

To find the exact value, we need to use a calculator set to degree mode or convert the angle to radians if the calculator is in radian mode. Here is the computation:

b = 2.4 * sin(44.2°) = 2.4 * 0.6946584 (approximately) = 1.66718 (approximately)

Thus, the value of 'b', the vertical component of the position vector in Cartesian coordinates, is approximately 1.67.