We're asked for the determine **tension**, the **net force**, the **acceleration **and **direction **of acceleration.

As usual for forces problems, we'll follow these steps:

- Draw a
**free body diagram (FBD)** - Set up Newton's Second Law equation (
**∑***F*=)**ma** **Solve**for the target variable

For this problem, we'll also need to do some conversion between **magnitude-angle** notation and **unit-vector** notation. Remember that in two dimensions, a force in unit-vector notation takes the form:

$\overline{)\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}{\mathbf{=}}{{\mathit{F}}}_{{\mathit{x}}}{\mathbf{}}\hat{\mathbf{i}}{\mathbf{+}}{{\mathit{F}}}_{{\mathit{y}}}{\mathbf{}}\hat{\mathbf{j}}}$

To calculate components from a magnitude and angle, we use the equations

$\overline{)\begin{array}{rcl}{\mathit{F}}_{\mathit{x}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}\mathbf{}\mathbf{cos}\mathbf{}\mathit{\theta}\\ {\mathit{F}}_{\mathit{y}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}\mathbf{}\mathbf{sin}\mathbf{}\mathit{\theta}\end{array}}$

To calculate the magnitude from components: $\overline{)\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{F}}\mathbf{\right|}{\mathbf{=}}\sqrt{{{\mathit{F}}_{\mathit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathit{F}}_{\mathit{y}}}^{\mathbf{2}}}}$

To calculate the angle from the components: $\overline{){\mathbf{tan}}{\mathit{\theta}}{\mathbf{=}}\frac{{\mathit{F}}_{\mathit{y}}}{{\mathit{F}}_{\mathit{x}}}}$

Tarzan, who weighs 820 N, swings from a cliff at the end of a 20.0 m vine that hangs from a high tree limb and initially makes an angle of 22.0° with the vertical. Assume that an *x* axis extends horizontally away from the cliff edge and a *y* axis extends upward. Immediately after Tarzan steps off the cliff, the tension in the vine is 760 N.

(*a*) Just then, what is the tension force acting on him from the vine in unit-vector notation?

What is the * net* force on him

(*b*) in unit-vector notation and

(*c*) in magnitude-angle notation?

(*d*) What are the magnitude and angle of Tarzan’s acceleration just then?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Forces with Unit Vectors concept. If you need more Forces with Unit Vectors practice, you can also practice Forces with Unit Vectors practice problems.

What textbook is this problem found in?

Our data indicates that this problem or a close variation was asked in Fundamentals of Physics - Halliday Calc 10th Edition. You can also practice Fundamentals of Physics - Halliday Calc 10th Edition practice problems.