Question 1010341: An aircraft carrier is traveling on a steady course East at 32 mph. Planes on the carrier have enough fuel for 3 hours of flight when traveling at a speed of 520 mph. One of the planes takes off at 90 degrees North. 1. How far will the plane have flown each hour? How far will the carrier have moved each hour? 2. So as to be able to catch the carrier and land at the instant that its fuel runs out,how soon does the pilot have to turn back to the ship and meet at it's new location?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! An aircraft carrier is traveling on a steady course East at 32 mph.
Planes on the carrier have enough fuel for 3 hours of flight when traveling at a speed of 520 mph.
One of the planes takes off at 90 degrees North.
:
1. How far will the plane have flown each hour?
520 mi. In 3 hrs the plane will travel 1560 mi
:
How far will the carrier have moved each hour?
32 mi. In three hrs the carrier travels 96 mi
:
2. So as to be able to catch the carrier and land at the instant that its fuel runs out, how soon does the pilot have to turn back to the ship and meet at it's new location?
:
A right triangle is formed a^2 + b^2 = c^2, where
a = distance plane traveled north
b = distance traveled by the carrier east
c = dist traveled by the plane to intercept the carrier after turning SE
we know
b = 96 mi
a + c = 1560 mi
c = (1560-a)
:
Pythag
a^2 + 96^2 = (1560-a)^2
a^2 + 9216 = 2433600 - 3120a + a^2
subtract a^2 from both sides, rearrange to:
3120a = 2433600 - 9216
3120a = 2424384
a = 2424384/3120
a = 777 mi north before turning SE
"how soon does the pilot have to turn back to the ship and meet at it's new location?"
777/520 = 1.49 hrs after take off. 1 hr 29 min (don't round up in this situation)
:
:
Confirm this; find the distance plane has to travel to intercept the ship
1520 - 777 = 783 mi
which takes 783/520 = 1.51 hrs
for a total of:
3 hrs
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