A particle moves in the plane in polar coordinates

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

A particle moves in the plane in polar coordinates (r,θ)(r,\theta), where the radial speed is constant drdt=5\dfrac{dr}{dt}=5 m/s and the angular speed is constant dθdt=0.5\dfrac{d\theta}{dt}=0.5 rad/s. At t=0t=0 the particle is at the point (4,0)(4,0), which corresponds to Cartesian coordinates (4,0)(4,0). Which of the following is the best approximation of the particle’s Cartesian position at t=2t=2 seconds? (a) ⟨14,1⟩\langle 14,1\rangle (b) ⟨11.8,7.6⟩\langle 11.8,7.6\rangle (c) ⟨7.6,11.8⟩\langle 7.6,11.8\rangle (d) ⟨12.3,6.7⟩\langle 12.3,6.7\rangle

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