Thread: Derivative Chain Rule Question.

Newton's Law states the force (F) exerted by a point with mass M on another points of mass m is F=GmM/r^2

Here G is a constant and r is the distance between the two points in meters. Let r be a function of time in seconds, where r(t) = 10^6sin( π t/300). (To clear confusion: r(t) equals to 10 to the power of 6 times sin( pi times t over 300))

What is the rate that F is changing with respect to time when t = 50, G = 6.673 x 10^-11 Nm^2/kg^2, m=70kg, and M = 6x10^24 kg?

Thank you for your time and help!

You have F = c*[1/r(t)]^2 = c * r(t)^(-2) where r(t) is a known function. What is the power rule for differentiation and can you use this?

F=GmM/r^2

G = 6.673 x 10^-11 Nm^2/kg^2,
m=70kg, and
M = 6x10^24 kg?

Then GmM is a constant in F=GmM/r^2
Let GmM = c for simplicity

F=cr^(-2)

dF/dt = -2c(r^(-3)) * dr/dt ...chain rule

r(t) = 10^6sin( π t/300)

dr/dt = r'(t) = 10^6*(π/300)*cos( π t/300)

Find r(5) and r'(5) by substituting t=5

Thank you guys for helping me out !