The minute and the hour hands on the face of a town clock ar

Solution

angular velocity of hour hand =2*3.14159/(60*12*60) = 0.000145443981
angular velocity of minute hand=2*3.14159/(60*60) = 0.00174532778

let L be the distance between the 2 hands.

by the cosine rule L^2 = (7^2)+(5^2)-2*7*5 cos (_h-_m) = sqrt(74 -70cos (_h-_m))

differentiate L, dropping the notation:

m-h at 9 o clock = (pi/2)

dL/dh =35 sin (h-m)/sqrt(74 -70cos (h -m))=4.06866736

dL/dm = -35 sin (h-m)/sqrt(74 -70cos (h -m))= -4.06866736

hence dL/dt = dL/d_h .(d_h/dt)+ dL/d_m.(d_m/dt)

= 4.06866736*0.000145443981 + -4.06866736*0.00174532778

= -0. 00650939499 ft/s