MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Two probes travel along the same straight tunnel. Probe P’s position (in meters) at time t seconds is sP(t)=12+6t−0.5t2 for 0≤t≤20. Probe Q is launched from the origin at t=0 with position function sQ(t)=4t+0.25t2 for the same interval. Positions are measured from the origin in the positive direction down the tunnel.
(a) Determine all times t in 0≤t≤20 when the two probes occupy the same point in the tunnel. Show all work leading to your answer.
(b) For each meeting time found in part (a), calculate the common position of the probes.
(c) At the earliest meeting time, find the magnitude of the relative velocity of Probe Q with respect to Probe P. Include appropriate units.