Homebrew Physics Problem: Projectile Motion with Camera Observation

[mettw]

I'm not sure if this is really the right forum for this, but the other forums insisted that all homework like posts should go here.

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^{o} and is tilted at an angle of 31^{o} 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?

 

[SammyS]

Is the camera at the same elevation as the gun?

Many mathematicians I know don't particularly like physics.

 

[mettw]

Is the camera at the same elevation as the gun?

Yes.

Many mathematicians I know don't particularly like physics.

I don't know if that would be a general feeling. After all, two of the millennium problems are physics problems.

 

[mettw]

Motion in 1 dimension - Problem 2

A skateboarder finds a long straight stretch of road of constant gradient. The road is 150m long and 100m down the hill is a speed camera. The skateboarder starts from rest at the top of the hill and as he passes the speed camera it goes off. Later in the local newspaper he sees the speed camera photo of himself with an article saying that he was photographed doing 65Km/h.

Neglecting air resistance and friction:

• What is the gradient of the hill as a percentage?
• How fast was he going when he reached the bottom of the hill?
• Are these results physically plausible? What does this say about the assumptions?