Question

1. Evaluate dF/dr when r=10,000, given that F= GmM/(r^2) and that F decreases by 3N/m when r=20,000.

2. The lowest point of a 5 meter long ladder is pulled away from a wall at 0.3 meters/sec. Find the rate at which the angle between the ladder and the wall changes when the ladder's lowest point is 3 meters away from the wall.

Answer 1

a. F=k/r^2

f'=-2k/r

df/dr=-2k/r

at r=20k

-3=-k/20000
k=60,000 N

so when r=10,000
df/dr=-60,000N/10,000m=-6N/m

CosTheta=x/5
-sinTheta*dTheta/dt=dx/dt *1/5

but sinTheta= sqrt(5^2-x^2)/25
sinTheta=sqrt(1-(x/5)^2)

solve4 for dThteta/dt