A ladder 10 m long reaches 8 m up a wall…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A ladder m long reaches m up a wall. Its foot is pulled m further away from the wall along the ground. How far does the top of the ladder slide down the wall?
Need a reminder? The key ideaShow
Pythagoras theorem: in a right triangle with the right angle at B, . The converse: if , the angle at B is a right angle. To find a hypotenuse, add the squares of the legs. To find a leg, subtract the square of the known leg from the square of the hypotenuse.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. At the start. The foot is m from the wall.
Step 2. After pulling. The foot is m from the wall.
Step 3. The new height. , so m.
Step 4. The slide. m.
Answer: the foot starts m from the wall, and the top slides down m.
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