a thin uniform rod of length l cm and a small particle lie on a line separared by a distance of a cm. if K is a positive constant and F is measured in newtons, the gravitational force between them is F=K/(a(a +l))
a) if a is increasing at the rate 2cm/min when a=15 and l=5, how fast is F increasing?
b)if l is decreasing at the rate 2cm/min when a =15 and l=5, how fast is F increasing?

Question

a thin uniform rod of length l cm and a small particle lie on a line separared by a distance of a cm. if K is a positive constant and F is measured in newtons, the gravitational force between them is F=K/(a(a +l))
a) if a is increasing at the rate 2cm/min when a=15 and l=5, how fast is F increasing?
b)if l is decreasing at the rate 2cm/min when a =15 and l=5, how fast is F increasing?

anonymous · Answer

Seems there needs to be some relation between l and a or dl/dt needs to be given in part a and da/dt needs to be given in part b). 

How to solve:

Re-write the equation: k(a^-1)(a+1)^-1
Use product rule and chain rule to find the derivative with respect to time: dF/dt= k(-1/a^2)(da/dt)(-(da/dt)+(dl/dt)/((a+1)^2))
Then plug in numbers:...