Question

a person walking in an airport terminal pulls a wheeled suitcase with a force of \\(20\text{ n}\\) upward and to the right, as shown in the figure below. the handle of the suitcase makes an angle of \\(73^\circ\\) with the horizontal. note that the figure is not drawn to scale.

write the force vector \\(\mathbf{f}\\) in the form \\(\mathbf{f} = a\mathbf{i} + b\mathbf{j}\\).

do not round any intermediate computations, and round the values in your answer to the nearest hundredth.

Explanation:

Identify given values and target

Using the Vector Components and Trigonometric Resolution knowledge points

$$
LATEXBLOCK0
$$

Calculate the horizontal component

Using the Vector Components knowledge point

$$
LATEXBLOCK1
$$

Calculate the vertical component

Using the Trigonometric Resolution knowledge point

$$
LATEXBLOCK2
$$

Construct the final vector

Using the Vector Components knowledge point

$$ \mathbf{F} = 5.85\mathbf{i} + 19.13\mathbf{j} $$

Answer:

\(\mathbf{F} = 5.85\mathbf{i} + 19.13\mathbf{j}\)