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?
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!
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