This problem gives students the opportunity to investigate projectile motion in a real-life context.
Pose the first question, to work out the optimum angle of release for the shot, bearing in mind that the shot is released from above ground level - perhaps discuss and agree as a group what height to assume the release takes place.
Once students have tackled this first question, ask them to identify the different assumptions they have made. The key assumption is that equal force can be applied at all release angles. Invite students to speculate what variables affect the force (and hence velocity) with which the shot can be launched.
Introduce the equation for release velocity varying with angle, and then invite students to calculate the range for different launch angles. This is best done numerically, as a spreadsheet task.
What are our modelling assumptions?
Are our assumptions valid?
Students may be interested in reading the article Modelling Assumptions in Mechanics.
Cannon Balls could provide a good introduction to thinking about the mechanics of motion under gravity.