Introduction to Classical Mechanics · Problem 1.16

Strategies for solving problems — Morin

Physics — Mechanics · limiting_cases_drag

Problem

Projectile with drag ** Consider a projectile subject to a drag force F=−mαv\mathbf{F} = -m\alpha \mathbf{v}. If it is fired with speed v0v_0 at an angle θ\theta, it can be shown that the height as a function of time is given by (just accept this here; it's one of the tasks of Exercise 3.53) y(t)=1α(v0sin⁡θ+gα)(1−e−αt)−gtα.y(t) = \frac{1}{\alpha}\left(v_0 \sin\theta + \frac{g}{\alpha}\right)\left(1 - e^{-\alpha t}\right) - \frac{gt}{\alpha}. Show that this reduces to the usual projectile expression, y(t)=(v0sin⁡θ)t−gt2/2y(t) = (v_0 \sin\theta)t - gt^2/2, in the limit of small α\alpha. What exactly is meant by "small α\alpha"?

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