Pam's eye-level height is 324 ft above sea level, and Adam's eye-level height is 400 ft above sea level. How much farther can Adam see to the horizon? Use the formula [tex]d=\sqrt{\frac{3 h}{2}}[/tex], with [tex]$d$[/tex] being the distance they can see in miles and [tex]$h$[/tex] being their eye-level height in feet.
Answer (1)
Calculate Pam's distance to the horizon: d P am = 2 3 × 324 = 486 .
Calculate Adam's distance to the horizon: d A d am = 2 3 × 400 = 600 .
Find the difference in distances: d d i ff ere n ce = 600 − 486 = 10 6 − 9 6 = 6 .
Adam can see 6 mi farther than Pam.
Explanation
Understanding the Problem We are given the formula d = 2 3 h to calculate the distance one can see to the horizon, where d is the distance in miles and h is the eye-level height in feet. We need to find the difference in the distances Adam and Pam can see.
Calculating Pam's Distance First, we calculate the distance Pam can see. Pam's eye-level height is 324 ft, so we substitute h = 324 into the formula: d P am = 2 3 × 324 d P am = 2 972 d P am = 486
Calculating Adam's Distance Next, we calculate the distance Adam can see. Adam's eye-level height is 400 ft, so we substitute h = 400 into the formula: d A d am = 2 3 × 400 d A d am = 2 1200 d A d am = 600
Finding the Difference Now, we find the difference in the distances they can see: d d i ff ere n ce = d A d am − d P am d d i ff ere n ce = 600 − 486 d d i ff ere n ce = 100 × 6 − 81 × 6 d d i ff ere n ce = 10 6 − 9 6 d d i ff ere n ce = ( 10 − 9 ) 6 d d i ff ere n ce = 6
Final Answer Therefore, Adam can see 6 miles farther than Pam.
Examples
Imagine you're on a coastal trip. Using the formula and the height of a cliff, you can estimate how far out to sea you can see. This is useful for navigation, spotting landmarks, or simply enjoying the view. Similarly, knowing the height of a lighthouse helps determine its visible range, crucial for maritime safety.
