Scenario: You want to launch a projectile with a cylindrical shape, radius r and length L. It is expected that the movement that the translational movement approaches a parabolic shot, but considering its shape, it can be modified
its trajectory. Consider that the initial speed of the projectile is v0 and that it is thrown at an angle q. Skip effects
friction with air.
1. Using the point object approximation, write an expression for the maximum height that the
projectile will hit. Obtain an expression for the range of the projectile and find the angle at which it
range is maximum.
2. Considering the cylindrical shape of the actual projectile and using the principle of conservation of energy,
both translational and rotational, obtain expressions analogous to those of the previous point, considering
that the object begins to rotate about its axis with a constant angular speed, w.
3. Now suppose that from the beginning of its trajectory, the projectile begins to rotate with an angular speed
constant s along its axis, in addition to having the angular speed w around its axis. Find
expressions for maximum height and reach What will happen to maximum height and reach with respect to
to the previous points?
4. Compare the expressions in items 1, 2, and 3, and answer the following questions: How do you modify
the maximum height that the projectile will reach, in which case it increases and in which it decreases? How do you modify
the range of the projectile, in which case it increases and in which it decreases? Discuss your answers.
5. Quantitatively compare cases 1 and 3 with the following values:
m = 20 kg, v0 = 100 m / s, q = 40º, r = 20 cm, L = 1 m, w = 1 rev / s, s = 0.5 rev / s.