Question

An airplane is flying at an altitude of 3,000 ft. The pilot dives 988 feet and then rapidly climbs 748 feet. The pilot then dives again 885 feet before making another climb of 1,099 feet. How far above or below an altitude of 3,000 feet is the airplane?

Answer 1

Given:

• An airplane is initially flying at an altitude of $3000ft.$
• The pilot "dives and climbs" two times to certain heights.

To find:

The final altitude of the airplane from it's initial altitude position.

Formulae to be used:

• From the given data, consider the diving as negative and apply subtraction formula for that, i.e., subtract that depth of diving from the previous altitude.
• Consider climbing as positive, and apply the addition formula for that, i.e., add that climbed altitude to the previous altitude.

Step-wise Solution:

Step-1:

The initial altitude of the flight = $3000ft.$

The, the pilot dives by a depth of $988ft.$

⇒ The present altitude of the flight is given by:

$=3000-988\\=2012ft.$

∴ The altitude of the flight after diving for the first time is $2012ft.$

Step-2:

The pilot after diving once, rapidly climbs by a height of $748ft.$

⇒ The present altitude of flight after climbing is given by:

$=2012+748\\=2760ft.$

∴ The altitude of the flight after first rapid climbing is $2760ft.$

Step-3:

Again, the pilot dives by a depth of $885ft.$

⇒The present altitude of the flight is given by:

$=2760-885\\=1875ft.$

∴ The altitude of the flight after diving for the second time is $1875ft.$

Step-4:

Later, the pilot climbs by a height of $1099ft.$

⇒The present altitude of the flight is given by:

$=1875+1099\\=2974ft.$

∴ The altitude of the flight after climbing for the second time is $2974ft.$

Step-5:

The difference of the present altitude of the airplane from the initial altitude is given by:

$=2974-3000\\=-26ft.$

⇒ The airplane after the two diving and climbing operations, is below the initial altitude by $26ft.$

Final Answer:

The final altitude of the airplane is $26ft.$ below the initial altitude.