Question

1. suppose there is a 1.1°f drop in temperature for every thousand feet that an airplane climbs into the sky. if the temperature on the ground is 59.7°f, what will be the temperature at an altitude of 11,000 ft?

Explanation:

Step1: Find the number of 1000 - ft intervals in 11,000 ft

To find how many thousand - foot intervals are in 11,000 ft, we divide the total altitude by 1000. So, the number of intervals \(n=\frac{11000}{1000} = 11\).

Step2: Calculate the total temperature drop

For each thousand - foot interval, the temperature drops by \(1.1^{\circ}\text{F}\). So, for 11 intervals, the total temperature drop \(d=1.1\times n\). Substituting \(n = 11\), we get \(d = 1.1\times11=12.1^{\circ}\text{F}\).

Step3: Calculate the temperature at 11,000 ft

The ground temperature \(T_{ground}=59.7^{\circ}\text{F}\). The temperature at altitude \(T = T_{ground}-d\). Substituting \(T_{ground}=59.7\) and \(d = 12.1\), we get \(T=59.7 - 12.1=47.6^{\circ}\text{F}\).

Answer:

The temperature at an altitude of 11,000 ft is \(47.6^{\circ}\text{F}\)