Chapter 9.3, Problem 34E

a.

To determine

To find: Total amount of wire required.

Answer to Problem 34E

Total amount of wire required including an extra 0.1 meter of wire at each attachment point is 1.6 meter.

Explanation of Solution

Given:

A tree to be supported by attaching three wires. One end of each wire to the tree at a point 1.2 meters above the ground, and the other end of each wire to a stake in the ground at appoint 0.5 meter from the tree.

Formula used:

Pythagoras theorem,

Hypotenuse = $\sqrt{p^2+b^2}$

Calculation:

Total amount of wire required,

  $\begin{array}{l}=\sqrt{{0.5}^2+{1.2}^2}\\ =1.3\end{array}$

Include an extra 0.1 meter of wire at each attachment point,

  $\begin{array}{l}=1.3+\left(\frac{10}{100}\times 3\right)\\ =1.6\end{array}$

Hence, total amount of wire required including an extra 0.1 meter of wire at each attachment point is 1.6 meter.

b.

To determine

To find:The height at which you can attach the wire.

Answer to Problem 34E

The height at which you can attach the wireallowing extra wire as described in part (a) is $1.41\text{ meters}$ .

Explanation of Solution

Given:

A tree to be supported by attaching three wires. One end of each wire to the tree at a point 1.2 meters above the ground, and the other end of each wire to a stake in the ground at appoint 0.5 meter from the tree.

Formula used:

Pythagoras theorem,

Hypotenuse = $\sqrt{p^2+b^2}$

Calculation:

Total length of wire = 4.2 meters

Number of supports to be given = 3

Therefore,

Length of each support,

  $\begin{array}{l}=\frac{4.2}{3}\\ =1.4\end{array}$

Hence, length of each support $=1.4$ meters.

By pythogoras theorem, find height

Height $=\sqrt{h^2-b^2}$

  $\begin{array}{l}=\sqrt{{1.4}^2-{0.5}^2}\\ =1.307\\ \approx 1.31\end{array}$

Hence, the height at which you can attach the wire is 1.31 meters

Allow the extra wire as described in part (a)

Therefore, the height at which you can attach the wireallowing extra wire as described in part (a) is,

  $\begin{array}{l}=1.31+0.1\\ =1.41\text{ meters}\end{array}$