Kevin Zhou — Mechanics I Problem 3 · Kevin Zhou #M1.3
Physics · mechanics
Problem
Problem 2. Now assume quadratic drag, F = −αmv2, which applies for fast-moving projectiles.
(a) Integrate Newton’s second law to get an implicit equation for v(t) with the same initial
conditions as above. That is, you don’t need to solve for v(t), as it’ll just make things messy.
(b) Your equation will only be valid when the projectile is going up; explain why.
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(c) Findv(t)foranobjectreleasedfromrestattimet = 0. (Hint: ifneeded,lookupsomestandard
integrals involving hyperbolic trigonometric functions. But don’t worry about memorizing
the results, since in competitions, any nontrivial integral needed will usually be given to you.)
(d) Integrate your answer to part (c) with respect to time to find y(t), and verify that the answer
makes sense at both small and large times.
Some people only call this quadratic case drag; they call the linear case viscous resistance. This is
because they behave fundamentally differently at the microscopic level, as we will explore in M7.