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mettw

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In his book "How to think like a Mathematician" Kevin Houston says that the best way to learn a subject is to create your own problems, since doing this requires far more understanding than simply selecting and applying the correct algorithm. So I thought I'd try my hand at creating some physics problems as I go through my old textbooks and post them online for anyone who is interested. Again, I apologise if this is the wrong forum for this.

**Problem mettw-1**

A camera at a proving ground has a field of view of 18[tex]^{o}[/tex] and is tilted at an angle of 31[tex]^{o}[/tex] to the horizontal. 9.9km distant a gun fires a shell directly up. The shell enters the field of view of the camera and then leaves it 15.6s later. The shell then explodes when it reaches its maximum possible height. Neglecting air resistance:

- At what height does the projectile explode?
- How long does it take to get there?
- What is the muzzle velocity of the gun?