What are the normal reactions?

Question

A ladder has a weight of 100N and is 5m long. Ursula and Valerie place the ladder on rough ground so that it makes an angle of 30˚ with a smooth wall as shown. Calculate (i) the normal reaction at the wall and (ii) the frictional force on the foot of the ladder. What is the direction of this frictional force?

Answer 1

I'm assuming the ladder was uniform

Let normal reaction at wall = Y, Frictional force = F

(i) take moments about the foot of the ladder:

2.5x100sin30 - 5Ycos30 = 0

2500sin30 = 5Ycos30

500tan30 = Y

Y = 500 / root(3)

Y = 289N (3sf)

(ii) Resolve horizontally:

F - Y = 0

F = Y

F = 289N (3sf) towards the wall

Answer 2

The direction of the frictional force is against the side of my head, it hurts!  I recommend therapy.