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Question

A 2.6 m long rod leans against a wall, its foot 1 meters from the wall. When the foot is moved a little away from the wall, its upper end slides the same length down. How much farther is the foot moved?


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Solution

Let the distance of the upper end of rod from ground be x.

The rod forms a right-angle triangle with the wall and ground.

So, using hypotenuse theorem:
2.62=12+x2
6.76=1+x2
5.76=x2
x=2.4

Given that upper end moves down the same distance as the lower end moves away.

Let the rod move y meters.

Using the hypotenuse theorem,
(2.4y)2+(1+y)2=2.62
5.764.8y+y2+1+2y+y2=6.76
2y22.8y+6.76=6.76
2y22.8y=0
2y(y1.4)=0
y=0 or y=1.4

But y can’t be equal to 0.
So, the foot of the rod moved 1.4 m further.


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