allegansveritatem
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- Joined
- Jan 10, 2018
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- 962
Here is the problem:
71 Distance between airplanes
An airplane flying north at 200 mi/hr passed over a point on the ground at 2:00 p.m. Another airplane at the same altitude passed over the point at 2:30 p.m., flying east at 400 mi/hr.
(a) If t denotes the time in hours after 2:30 p.m., express the distance d between the airplanes in terms of t.
(b) At what time after 2:30 p.m. were the airplanes 500 miles apart?
I was able to come up with the notion that the Pythagorian Theorem was going to be involved for part (a) but...well, here is what I got for part (a):
and here is the solution from the solutions manual:
I am able to follow this until I get just beyond the 3rd equals sign. Then the train jumps the rails and I am stuck in the mud. How did the author ever go from the term under the second radical sign to the quadratic equation under the third radical sign??? How is that even possible? I fault the solutions manual on this one: What business had the author of the manual to go eliding so egregiously?
PS: I admit that my solution owes much to the solutions manual. I couldn't have even gotten it, wrong though it is, without some initial guidance.
71 Distance between airplanes
An airplane flying north at 200 mi/hr passed over a point on the ground at 2:00 p.m. Another airplane at the same altitude passed over the point at 2:30 p.m., flying east at 400 mi/hr.
(a) If t denotes the time in hours after 2:30 p.m., express the distance d between the airplanes in terms of t.
(b) At what time after 2:30 p.m. were the airplanes 500 miles apart?
I was able to come up with the notion that the Pythagorian Theorem was going to be involved for part (a) but...well, here is what I got for part (a):
and here is the solution from the solutions manual:
I am able to follow this until I get just beyond the 3rd equals sign. Then the train jumps the rails and I am stuck in the mud. How did the author ever go from the term under the second radical sign to the quadratic equation under the third radical sign??? How is that even possible? I fault the solutions manual on this one: What business had the author of the manual to go eliding so egregiously?
PS: I admit that my solution owes much to the solutions manual. I couldn't have even gotten it, wrong though it is, without some initial guidance.
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