After 28 sec. the plank will be 12 - (1/4)(28) = 12 - 7 = 5 meters from the wall
For the second part...we have that
x^2 + y^2 = r^2 take the derivative with respect to time
2x (dx/dt) + 2y (dy/dt) = 2r(dr/dt)
r = 13 m
dr/dt = 0 [the plank length is not changing ]
dx/dt = -1/4 m/s
At 28 sec, x = 5 meters and y = sqrt (13^2 - 5^2) = sqrt (169 - 25) = sqrt (144) = 12 meters
dy/dt = what we are looking for
So we have
2(5m)(-1/4 m/s) + 2(12m)(dy/dt) = 0
(10m) (-1/4 m/s) = - (24m)(dy/dt)
-2.5 (m^2/s) = (-24m) (dy/dt)
2.5 m^2/s = (24m) (dy/dt) divide both sides by 24 m
(2.5/24)(m/s) = dy/dt
(5/48)m/s = dy/dt