Curves & Motion in space?

Question

I'm stuck on 2 HW problems. This is for my Calc III class.

1) A projectile from the origin is to be fired at a target 600 feet away. There is a hill 300 feet high midway between the gun site and this target. At what initial angle of inclination should the projectile be fired?

*My guess to approach this is: Will this be a 2-part problem? Solving for an angle from origin to 300 ft then from 300 ft to 600? I don't know how to start exactly.

2) A point moves on a circle whose center is at the origin. Use the dot product to show that the position & velocity vectors of the moving point are always perpendicular.

*I know the answer is scalar, and must be 0 for the vectors to be perpendicular. That's as far as I can get for now. I will keep trying things till tomorrow morning (the last time I can check here before turning in these in).

Any helpful suggestions for either problem or both will be greatly appreciated. Thank you for your time and help! :)

Answer 1

See my answers in the mathematics section.