Homework SourseThe hands of a clock in some tower are approximately 25m and
The hands of a clock in some tower are approximately 2.5m and 1.5m in length. How fast is the distance between the tips of the hands changing at 9:00? Hint, use the law of cosines
The distance between the tips of the hands is changing at a rate of ? m/hr at 9:00
The distance between the tips of the hands is changing at a rate of ? m/hr at 9:00
Solution
consider x^2 +y^2 =z^2
differentiate w.r.t time we get
x(dx/dt)+ y(dy/dt) = z(dz/dt)
here x=1.5 y=2.5 z=2.915
consider perimeter of clock 2*pie* 2.5
then each degree will be equal to (5pie/60)m let this be \"A\"
dx/dt =5A m/hr
dy/dt = 60A m/hr
hence solve for dz/dt we get 54.03A
