A glider begins its flight 1½ mile above the ground. After 60 minutes, it is (9/10) mile above the ground. Find the change in height of the glider.
If it continues to descend at this rate, how long does the entire descent last?
- The change in height is
- The entire descent lasts
Answer
1) The change in height = 0.6 mile or (3/5) mile
2) The entire descent lasts 2.5 hours or 2 hours 30 minutes.
Explanation
We first calculate the change in height.
The glider initially is at a height of 1½ miles.
Then, after 60 minutes, the glider's height is (9/10) mile.
The change in height = (Initial Height) - (New Height after descent)
The change in height = (1½ miles) - (9/10) mile
Note that
1½ = (3/2) = 1.5
(9/10) = 0.9
The change in height = 1.5 - 0.9 = 0.6 mile
0.6 mile = (6/10) mile = (3/5) mile
We can then calculate the time that the entire descent lasts.
To do this, we need to first calculate the rate at which the glider descends.
In 60 minutes, the glider descends 0.6 mile (The change in height during descent)
Rate of descent = (Change in height during decsent) ÷ (Time taken)
Change in height during decsent = 0.6 mile
Time taken = 60 minutes
Rate of descent = 0.6 ÷ 60 = 0.01 mile/minute
The entire descent would require the glider to go from the initial height of 1½ miles to the ground level (0 miles).
We are told that the rate of descent is constant at 0.01 mile/minute.
Recall that,
Rate of descent = (Change in height during decsent) ÷ (Time taken)
Time Taken = (Change in height during descent) ÷ (Rate of Descent)
Time Taken for the entire descent = ?
Change in height durinh entire descent = 1.5 mile - 0 mile = 1.5 miles
Rate of descent = 0.01 mile/minute
Time taken for the entire descent = 1.5 ÷ 0.01 = 150 minutes = 2.5 hours or 2 hours 30 minutes.
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