Couple simple problems

I just wrote a physics exam today and I got stumped on a couple problems that have been bugging me, and I should probably find out how they are done the right way, or at least how to set them up just in case I use them again and I don't see any examples in my textbook:

The first I'm pretty sure involves a quadratic. It involves finding the angle you need to tilt a gun up in order to hit a target a distance d away if the target is on the same level as you. Only the Vi from the gun (without components) and the distance away are given.


The second is a torque question I think. Determine if a glass will tip over when a horizontal force is applied to the top rim and the coefficient of static friction is 0.2. The glass weighs w has height h and has diameter d.

 

The distance equations for each component are

Given Vi

(1) Viy = Vi*sin(Θ) -1/2 (9.81)t^2

(2) Vix = Vi*cos(Θ) *t

I tried stating that

t = Vix/(Vi*cos(Θ))

and putting that in equation (1) for t and I get lost after I end up with sin(Θ) and cos(Θ)

I can't find examples of this problem in by textbook or notes so it's possible there is a much better approach.


For the second problem the frictional force is just w(0.2) and acts in the direction resisting motion. The force that acts on the top rim acts at a distance to a pivot (I think) Possibly at the center of the glass.

 

The center of mass must go beyond the vertical from the edge of the cup that remains on the table, but I'm unsure of how to include gravity and the two forces in order to understand how the system will evolve when you push on the cup.

This is a torque question isn't it?