Chapter 9.4, Problem 73AYU

To determine

To express: the force vector Fin terms of i and j.

Answer to Problem 73AYU

  $\text{F}=20\sqrt{3}\text{i}+20\text{j}$ .

Explanation of Solution

Given:

The force pulls a wagon by a child is $\text{F}=40\text{ pounds}$ .

And the angled makes by the handle of the wagon is ${30}^{\circ }$ with the ground.

Calculation:

As it is known that,

Components of force vector are

  $\begin{array}{l}{F}_i=40\cos {30}^{\circ }=40\left(\frac{\sqrt{3}}{2}\right)=20\sqrt{3}\{\cos {30}^{\circ }=\frac{\sqrt{3}}{2}\}\\ F_i=40\sin {30}^{\circ }=40\left(\frac{1}{2}\right)=20\{sin{30}^{\circ }=\frac{1}{2}\}\end{array}$ .

Thus, the force vector is $\text{F}=20\sqrt{3}\text{i}+20\text{j}$ .

Hence, the force vector is $\text{F}=20\sqrt{3}\text{i}+20\text{j}$ .