Challenging Problems

You're good if you can get these two:

1. Two planes are flying at 32,000 feet moving directly toward a point above a control tower. The first plane is 100 miles from being directly above the tower and the second is 220 miles from being directly over the tower. The angle between them is 120 degrees. If the first plane is moving at 320 mph and the second plane is moving at 400 mph, how fast is the distance between the two planes decreasing (see figure 1)?
2. A system is positioned on a ramp according to figure 2. The mass of m₁ is equal to 8.0 kg and the mass of m₂ is equal to 23.0 kg. m₁ is pulled directly upwards by a magnet with a force of 8.5 N. The coefficient of kinetic friction μ for m₁ is 0.370. μ for m₂ is 0.289. (a) Find the acceleration of the system. (b) How much time will it take for m₁ to reach the top of the ramp?

Figure 1:

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Figure 2:

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The latter of the two is one I made up myself. It's easy to make up physics problems... but solving them is another story.

I'll tell you right now that the first one is not solvable without knowledge of trig formulas and calculus. The second problem just requires basic trig knowledge (SOHCAHTOA), and kinematic equations.

I'll post hints sometime this week, and will hopefully have the solutions all worked out by next weekend!