Introduction to Classical Mechanics · Problem 3.53

Using F = ma — Morin

Physics — Mechanics · projectile_with_drag

Problem

Projectile with drag *** A ball is thrown with speed v0v_0 at an angle θ\theta. Let the drag force from the air take the form Fd=−βv≡−mαv\mathbf{F}_d = -\beta \mathbf{v} \equiv -m\alpha \mathbf{v}. (a) Find x(t)x(t) and y(t)y(t). (b) Assume that the drag coefficient takes the value that makes the magnitude of the initial drag force equal to the weight of the ball. If your goal is to have xx be as large as possible when yy achieves its maximum value (you don't care what this maximum value actually is), show that θ\theta should satisfy sin⁡θ=(5−1)/2\sin \theta = (\sqrt{5} - 1)/2, which just happens to be the inverse of the golden ratio.

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