fill in the blank question\nvector a points along the positive x - axis and has a magnitude of 22.0 km…

fill in the blank question\nvector a points along the positive x - axis and has a magnitude of 22.0 km. vector b points counterclockwise from the positive x - axis at an angle of 58° with a magnitude of 17.0 km. the magnitude of the resultant vector is found to be 34.2 km. the direction of the resultant vector will be rotated counterclockwise from the positive x - axis. (round to three significant figures.)\nneed help? review these concept resources.\nread about the concept

fill in the blank question\nvector a points along the positive x - axis and has a magnitude of 22.0 km. vector b points counterclockwise from the positive x - axis at an angle of 58° with a magnitude of 17.0 km. the magnitude of the resultant vector is found to be 34.2 km. the direction of the resultant vector will be rotated counterclockwise from the positive x - axis. (round to three significant figures.)\nneed help? review these concept resources.\nread about the concept

Answer

Explanation:

Step1: Calculate the x - component of vector (B)

The x - component of a vector (B) with magnitude (B = 17.0) km and angle (\theta=58^{\circ}) is (B_x=B\cos\theta). [B_x = 17.0\cos(58^{\circ})] [B_x=17.0\times0.5299 = 9.0083]

Step2: Calculate the total x - component of the resultant vector (R)

The x - component of vector (A) is (A_x = 22.0) km (since it is along the x - axis). The total x - component of the resultant vector (R_x=A_x + B_x) [R_x=22.0+9.0083 = 31.0083]

Step3: Calculate the y - component of vector (B)

The y - component of vector (B) is (B_y=B\sin\theta) [B_y = 17.0\sin(58^{\circ})] [B_y=17.0\times0.8480=14.416]

Step4: Use the formula for the direction of a vector

The direction (\alpha) of the resultant vector is given by (\tan\alpha=\frac{R_y}{R_x}). Since (R_y = B_y) (because (A) has no y - component) (\tan\alpha=\frac{14.416}{31.0083}) (\alpha=\arctan\left(\frac{14.416}{31.0083}\right)) [ \alpha=\arctan(0.4649)] [ \alpha = 25.0^{\circ}]

Answer:

(25.0^{\circ})