I’ve heard several stories from Dan and Paulo about an infamous question on the Fall 2000 Physics 1 (16.105) final exam, back when there were still long-answer questions. Now that Ryan is about to graduate, he brought in his whole collection of old exams, and this exam (and question) turned up.

Here it is, for anyone who might wish to solve it (if it’s possible — I think it might be, using conservation of momentum and energy).

A cannon of mass M fires a shell of mass 2 kg at an initial speed of 55 m/s (relative to the ground) at an angle θ over a smooth horizontal surface [as shown in the figure]. The horizontal range R is 290 m. The cannon recoils horizontally with a kinetic energy equal to 1% (i.e. 1/100) of that of the shell. When the angle of launch is increased by 5° (with the same initial speed of the shell), the kinetic energy of the cannon is found to be 0.76% of that of the shell. Use these data to find the mass M of the cannon.

Based on the figure, it should be safe to assume that the shell lands at the same elevation it was launched from (i.e. the cannon lies on a large, flat plane).

Good luck, and please post your solutions in the comments.

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