Question

The minute hand on a watch is 9 mm long and the hour hand is 5 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.) mm/h

Answer 1

Minute hand 9mm Hour Hand 5mm c2 = a2 + b2 - 2abcosC c2 = 92 +52 - 2 * 9 *5 cosC c2 = 96 - 90 cosC 2c dc/dt = 90 sinC dC/dt at one o'clock: C = 30 degrees=> sin(30) = 1/2 dC/dt = 2pi - pi/6 = 11pi/6 => -11pi/6 c2= 96 - 90 cos (30) c = âš(96 -45âš3) 2 dc/dt = 90 * 1/2 * -11pi/6 dc/dt = -25 mm/h hence the distance between hands is decreasing at 25 mm/hr