Question

The minute hand on a watch is 8 mm long and the hour hand is 6 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 rough sketch for hour hand and minute hand is shown as below:

6 8

The hour hand trawels around the clock at |revoluti on 2 radian π 12h 12h The minute hand travels around the clock at |revolution 2 radian . T rad/ h So, the angle θ between them is changing at 11π dD The objective is to find at one o' clock. At one o'clock, the minute handis at 12, the hour handis at 1, which is _ ofa revolution dt So, at one o'clock. θ -. 2π θ From cosine rule in the triangle D. 62 +82-2 (6) (8) cos θ D2- 100-96 cose Differentiate both si des with respect tot dD 2D_-O-96(-sin θ)- dt dt dt 2D dt dt D dt

Put θ--in equation (3)'s 兀 D-100-96 cos- → D = 100-96 Now, substitute D-100 dt= 6_ , g=-,In equation (4 ) dD 48sin 6 dte dt D dt 48sin 100-48/3 48 兀 11π 11T 100-483 6 =-33.66306511 33.7mm /h (Or) 33.7 3600 0.009361 mm / s