Chapter 6.9, Problem 9PPS

(a)

To determine

To draw: a diagram of the situation.

Explanation of Solution

Given information:

Consider the following situation. A biplane starts to take off from the beginning of a runway. When the plane is level with the end of the runway, it is 500 feet above the ground. A bird is flying in the same direction. It is 8 feet above the ground and 15 feet from the beginning of the runway.

Calculation:

Plane is at a height of $500\text{ft}$ .

Bird is at a height of $8\text{ft}$ .

Bird is $15\text{ft}$ away from the beginning of the runway.

Draw the situation.

Let plane is $x\text{ft}$ away from the beginning of the runway.

Graph is as shown below.

  

(b)

To determine

To find: the distance of the plane from the beginning of the runway.

Answer to Problem 9PPS

  $937.5$ ft.

Explanation of Solution

Calculation:

From the similarity of triangles,

  $\frac{500}{x}=\frac{8}{15}$

Apply the cross multiplication and solve.

  $\begin{array}{c}8\times x=500\times 15\\ x=\frac{500\times 15}{8}\\ x=937.5\end{array}$

Hence, the result is $937.5$ ft.