Implicit differentiation of a clock face

Question

The hour hand of a clock is 5 inches long and the minute hand is 7 inches long. At the moment the hour hand is positioned at 3 and the minute hand is positioned at 7, what is the instantaneous rate of change of the distance between the tip of the hour hand and the tip of the minute hand? Express the rate of change in inches per second, and round your answer to four decimal places.

Answer 1

i would argue that you can simply perform vector addition us the speed of the tip of each hand to get the correct answer. note that the actual distance between the hands does not matter, just the rate of change. the hour hand goes through 2Pi in 12 hours, etc for the minute hand. tangential speed is v=wr. the just add/subtract the velocity vector and that will tell you have fast the tips are moving away from each other.