Question

Suppose there is a 1.7f drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on the ground is 49.9f what will be the temperature when the plane reaches am altitude of 4,000ft?? The temperature will be_____F (type an integer or a decimal)

Answer 1

`43.1 ^(\circ)F`

Explanation:

Give that for every 1000 feet increase in the height there is a drop of
`1.7 ^(\circ)F` in temperature.

So, the rate of temperature drop with respect to height, R = 1.7/1000
`^(\circ)F/\text{ft}`.

If the change in height is
`\Deltah`
`\Delta h` feet, the temperature drop,

`\Delta T= \Delta h R \;^(\circ)F\cdots(i)`

The temperature on the ground is 49.9
`^(\circ)F`.

At the ground, the height is 0, so the change in height, \Delta h when the plane reaches an altitude of 4,000 feet, is

\Delta h =4000-0=4000 feet

Now, from equation (i), the temperature drop

`\Delta T= 4000 * \frac {1.7}{1000}=6.8\;^(\circ)F.`

Hence, the temperature at an altitude of 4000 feet
`= 49.9-6.8=43.1 \;^(\circ)F`.