Difference between revisions of "2023 SSMO Team Round Problems/Problem 2"
(Created page with "==Problem== A plane and a car start both move northward. The car moves northbound at 60 miles per hour. The plane moves northeast and increases in altitude at an angle of <mat...") |
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==Solution== | ==Solution== | ||
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| + | Suppose the plane moves at speed <math>s</math>. Its purely horizontal component is then <cmath>\frac{\sqrt{3}}{2}s,</cmath> and the northward part of this horizontal velocity is | ||
| + | <cmath>\frac{\sqrt{3}}{2\sqrt{2}}s = 60.</cmath> | ||
| + | |||
| + | Thus, | ||
| + | <cmath>\frac{3}{8}s = 3600,</cmath> | ||
| + | so | ||
| + | <cmath>s = \boxed{9600}.</cmath> | ||
| + | |||
| + | ~SMO_Team | ||
Latest revision as of 21:16, 9 September 2025
Problem
A plane and a car start both move northward. The car moves northbound at 60 miles per hour. The plane moves northeast and increases in altitude at an angle of 
Let 
the speed in feet per second that the plane must fly at to move north at the same speed as the car. Find 
.
Solution
Suppose the plane moves at speed . Its purely horizontal component is then ![\[\frac{\sqrt{3}}{2}s,\]](http://latex.artofproblemsolving.com/d/1/7/d1710888bcef816160d25130fe2534e1bf0a845f.png)
and the northward part of this horizontal velocity is
![\[\frac{\sqrt{3}}{2\sqrt{2}}s = 60.\]](http://latex.artofproblemsolving.com/2/9/0/2903f2c8b0c10b4b30d96d85c78cfc699338f78d.png)
Thus,
![\[\frac{3}{8}s = 3600,\]](http://latex.artofproblemsolving.com/2/f/e/2fef0e447ffa9444319962f22d0803314db2bda8.png)
so
![\[s = \boxed{9600}.\]](http://latex.artofproblemsolving.com/1/d/b/1dbd4b7fb2f34eb8110e17b77e7a13dded1d8324.png)
~SMO_Team
