Chapter 11, Problem 83A

To determine

To Calculate: Chimp’s speed when it reaches the ground.

Answer to Problem 83A

  $v=8.6\text{ m/s}$

Explanation of Solution

Given info:

Length of vine, $l=13\text{ m}$

Angle, $\theta ={45}^o$

Formula used:

Kinetics energy:

  $K.E=\frac{1}{2}m{v}^2$

Potential energy:

  $P.E=mgh$

Calculation:

Height from the ground at $4{\text{5}}^{\text{o}}$ :

  $\begin{array}{c}h=l-l\cos {45}^o\\ =13-13\cos {45}^o\\ =3.80\text{ m}\end{array}$

Applying the conservation of energy:

Kinetics energy gain = potential energy lost

  $\begin{array}{l}\frac{1}{2}m{v}^2=mgh\\ \Rightarrow v=\sqrt{2gh}\end{array}$

Plugging in the given values:

  $\begin{array}{c}v=\sqrt{2\times 9.8\times 3.80}\\ =8.6\text{ m/s}\end{array}$

Conclusion:

Speed of chimp when it reaches the ground: $8.6\text{ m/s}$