# Problem: 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?

###### FREE Expert Solution

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:

1. Draw a free body diagram (FBD)
2. Set up Newton's Second Law equation (Fma )
3. 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:

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

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

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

79% (314 ratings) ###### Problem Details

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?