A projectile is launched at time

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

Problem

A projectile is launched at time t=0t=0, and its velocity for t≥0t\ge 0 is v(t)=⟨4cos⁡t, 4sin⁡t, t⟩\mathbf v(t)=\langle 4\cos t,\,4\sin t,\,t\rangle. At time t=πt=\pi, its position is r(π)=⟨6, −2, 7⟩\mathbf r(\pi)=\langle 6,\,-2,\,7\rangle. What is r(2π)\mathbf r(2\pi)? (a) ⟨6,6,3π22+7⟩\langle 6,6,\tfrac{3\pi^2}{2}+7\rangle (b) ⟨6,−10,3π22+7⟩\langle 6,-10,\tfrac{3\pi^2}{2}+7\rangle (c) ⟨6,−10,3π2+7⟩\langle 6,-10,3\pi^2+7\rangle (d) ⟨10,−2,3π22+7⟩\langle 10,-2,\tfrac{3\pi^2}{2}+7\rangle

Related theory

Browse the problem library