The minute hand on a watch is 9 mm long and the hour hand is 7 mm long. How fast is the distance between the tips of the hands changing at one o'clock? (Round your answer to one decimal place.)

Answer 1

The equations for the minute and hour hands tips' motions are

x = (cosωt,–sinωt)r

and

X = (cosΩt,–sinΩt)R

respectively, where r = 0.009m, R = 0.007m, 2π/ω = 60·60s and 2π/Ω = 12·60·60s.

The "–" sign is for clockwise rotation.

You are asked to compute (d/dt)|x – X| at one o'clock, when ωt = π/2 and Ωt = π/3.

Answer 2

Use the Law of Cosines and determine dc / dθ, when θ = π / 6.