To get up on the roof, a person with a mass m=75kg they use a aluminum ladder (mass 12.5kg and length 6.0m) against a house on a concrete pad with the base of the ladder 2m from the house. The ladder rests against a plastic rain gutter, which we can assume to be frictionless, so the force from the gutter on the ladder acts perpendicularly to the ladder. The center of mass of the ladder in 2m from the bottom. The person is standing 3m from the bottom.

part (a) what is the magnitude of the force in newtons on the ladder at the top?

part (b) what is the magnitude of the force in newtons on the ladder at the bottom?

The angle between the ladder and the base:

cos α = 6 m / 2 m = 1/3

α = cos^ (-1) 1/3 = 70.53°

Ft - magnitude of the force at the top;

Fb - magnitude of the force at the bottom.

F b * cos α - 12.5 * g * cos α - 75 * g * cos α + F t = 0

1/3 F b - 40.875 - 245.25 + F t = 0

1/3 F b + F t = 286.125 N

h = √ (6² - 2²) = √32 = 4√2

2 : x = 4√2 : 6, x = 3√2 / 2

3 : y = 4√2 : 6, y = 9√2 / 4;

M b = F t * 6 m - 12.5 kg * 9.81 m/s² * cos α * 3√2 / 2 - 75 kg * 9.81 m/s² * * cos α * 9√2 / 4 = 0

6 F t = 86.72 + 780.38

6 F t = 867.1

F t = 867.1 : 6

Part A) F t = 144.5 N

1/3 F b + 144.5 = 286.125

1/3 F b = 141.625

F b = 141.625 * 3

Part B) F b = 424.875 N