SOLUTION: An airplane takes off at a 15° angle and travels at the rate of 350 ft/sec. Approximately how long does it take the airplane to reach an altitude of 25,000 feet? (Round your answer

Algebra ->  Trigonometry-basics -> SOLUTION: An airplane takes off at a 15° angle and travels at the rate of 350 ft/sec. Approximately how long does it take the airplane to reach an altitude of 25,000 feet? (Round your answer      Log On


   

Question 924982: An airplane takes off at a 15° angle and travels at the rate of 350 ft/sec. Approximately how long does it take the airplane to reach an altitude of 25,000 feet? (Round your answer to two decimal places.)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you draw out the triangle, you get



* y is the height of the airplane at time t (y is the opposite side)

* 350t represents how far along the hypotenuse the plane has traveled

* t is time in seconds

-------------------------------------------------------

From the drawing above, we see

opposite = y

hypotenuse = 350t

-------------------------------------------------------

So that means we can say


sin(theta) = opposite/hypotenuse


sin(15) = y/350t


sin(15) = y/350t


350t*sin(15) = y


(350*sin(15))*t = y


y = (350*sin(15))*t

-------------------------------------------------------

The function y+=+%28350%2Asin%2815%29%29%2At represents how high the plane is at time t.

y is the vertical distance.
t is time in seconds.

-------------------------------------------------------

Plug in y = 25,000 and solve for t


y+=+%28350%2Asin%2815%29%29%2At


25000+=+%28350%2Asin%2815%29%29%2At


25000%2F%28350%2Asin%2815%29%29+=+t


t+=+25000%2F%28350%2Asin%2815%29%29


t+=+275.978807511162 ... use a calculator here (type in "25000/(350*sin(15))" without quotes).

Special Note: make sure you're in degree mode and NOT in radian mode.


t+=+275.98 ... round to 2 decimal places


It takes approximately 275.98 seconds for the airplane to climb to 25,000 ft. So that is your answer.


Note: 275.98 seconds = 4 minutes, 35.98 seconds = 4.6 minutes (approximate). This is extra info to possibly think of the timeframe in an easier context.