a shopper pushes a grocery cart with a force of 55 n downward and to the right, as shown in the figure…

a shopper pushes a grocery cart with a force of 55 n downward and to the right, as shown in the figure below. the angle the handle makes with the horizontal is 33°. note that the figure is not drawn to scale. write the force vector f in the form f = ai + bj. do not round any intermediate computations, and round the values in your answer to the nearest hundredth.

a shopper pushes a grocery cart with a force of 55 n downward and to the right, as shown in the figure below. the angle the handle makes with the horizontal is 33°. note that the figure is not drawn to scale. write the force vector f in the form f = ai + bj. do not round any intermediate computations, and round the values in your answer to the nearest hundredth.

Answer

Explanation:

Step1: Find the horizontal - component

The horizontal component $a$ of the force vector $\mathbf{F}$ is given by $F\cos\theta$, where $F = 55$ N and $\theta=33^{\circ}$. So, $a = 55\cos33^{\circ}$. $a=55\times0.8387 = 46.13$ (rounded to the nearest hundredth)

Step2: Find the vertical - component

The vertical component $b$ of the force vector $\mathbf{F}$ is given by $F\sin\theta$. Since the force is downward, $b=- 55\sin33^{\circ}$. $b=-55\times0.5446=-29.95$ (rounded to the nearest hundredth)

Answer:

$\mathbf{F}=46.13\mathbf{i}-29.95\mathbf{j}$