Question

A 2.6-meter long rod leans against a wall, its foot 1 meter 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?

Answer 1

PQ = 1m

RQ = 2.6m

\(PR=\sqrt{RQ^2-PQ^2}\)

= \(\sqrt{2.6^2-1^2}\)

= \(\sqrt{6.76-1}\) = \(\sqrt{5.76}=2.4\)

PR = 2.4m

RX = a, PY = 1 + a

XY = 2.6

PX = 2.4 - a

PX² + PY² = XY²

(2.4 - a)² + (1 + a)² = 2.62

5.76 - 4.8a + a² + 1 + 2a + a² = 6.76

2a² - 2.8 a = 0; a² - 1.4a = 0; a - 1.4 = 0; a = 1.4

Length the rod has moved = 1.4m