Sliding ladder whose top speeds up

A ladder of length \(5\) m leans against a vertical wall, with its foot on horizontal ground. The foot is pulled away from the wall at a constant rate of \(0.5\) m/s. At time \(t\) seconds, the foot is \(x\) m from the wall and the top is \(y\) m above the ground.

1. Show that \(\dfrac{\mathrm dy}{\mathrm dt}=-\dfrac{x}{2\sqrt{25-x^2}}\).[3]
2. Find the speed of the top of the ladder when \(x=3\) and when \(x=4\).[2]
3. Find the exact value of \(x\) at which the top of the ladder moves at the same speed as the foot.[2]
4. Describe what the formula in (a) predicts as the top of the ladder approaches the ground, and explain why the model cannot hold up to that moment.[2]