Chapter 10.2, Problem 48PPE

(a)

To determine

Find the distance to the horizon from a height of 150 feet, 225 ft, 300 ft

Answer to Problem 48PPE

  $d_1=15miles$

  $d_2\approx 18miles$$d_3\approx 21miles$

Explanation of Solution

Given:

From a viewing height of h feet, the approximate distance d to the horizon, in miles, is given by the equation $d=\sqrt{\frac{3h}{2}}$ .

Calculation:

Substitute the given 3 heights in the formula and find the distance, d :

  $d_1=\sqrt{\frac{3(h_1)}{2}}=\sqrt{\frac{3(150)}{2}}=\sqrt{225}=15miles$

  $d_2=\sqrt{\frac{3(h_2)}{2}}=\sqrt{\frac{3(225)}{2}}=\sqrt{337.5}\approx 18miles$

  $d_3=\sqrt{\frac{3(h_3)}{2}}=\sqrt{\frac{3(300)}{2}}=\sqrt{450}\approx 21miles$

(b)

To determine

Find the distance to the horizon increases as the height increases.

Answer to Problem 48PPE

The distance to the horizon increases by 3 miles as the height increases by 75 feet.

Explanation of Solution

Calculation:

From part (a),

  $d_{150}=15miles$

  $d_{225}\approx 18miles$

  $d_{300}\approx 21miles$

So, we observe , as the height increases by 225-150 = 300-225 = 75 feet , the distance from the origin increases by 18-15 = 21-18 = 3 miles.