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Physic

Cannon Ball Experiment

Consider the problem of hitting a specified target value. For a cannon ball that is fired at a target, the equation of flight is given by

y = ((F/m)² sin 2a)/g

where F is the thrust, m is the mass of the cannon ball, a is the angle of projection and g is acceleration due to gravity.

If the target distance y is 150 metres, the mass of the cannon ball is 0.2 kg, g is 9.81 m s -2 what is the best value of thrust (F) and angle of projection (a)?

Most engineers are quick to assign a value of F (say 10 N) and then calculate the angle a = 0.5 sin -1 [y g (m / F) 2 ]. Is this the best answer?

Certainly not. In reality, F, m and a will all have some variability. The objective is to find those values of F and a (assuming for simplicity that m can be accurately determined) that will consistently hit the target despite variations in F or a.

How do we do it?

Our strategy is as follows:

Instead of merely calculated F and a, an engineer can include variability into the equation and calculate F and a that are robust to not only variations in F and a but also air resistance, wind directions, etc. The results of the conventional design and parameter design are shown above.

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