Understanding Engineering Mathematics

bank, a pole can be set atJ on the intersection of the linesEGand

HCproduced backwards. Show thatJG=FH.

(c) The lineABcrosses the river on the skew and poles placed atF and

Gon the near and far banks respectively.DF is set out along the

near bank, soGFis perpendicular toGF. A perpendicular fromDis

constructed to meetABatC. Show that

EG=

CE×EF

ED

Discuss the relative merits of each of the methods.

2.A railway track floor is cut into the side of a hill with slope 1 ink. Both sides of the
cutting have slope 1 inm. If produced into the earth the slopes of the cutting intersect
at a pointG(see Figure 5.27). The flat horizontal bed of the cutting is at a depthh
below the point where the centre lineGLintersects the line of the slope of the hill.
The width of the cutting floor isb.

h

b

2

b

2

G

C

w 2 w 1

L

E

1 in k

1 in

m

Figure 5.27

Show that the distance,w 1 from the up-slope edge of the cutting to the centre lineGL

is given by

w 1 =

(

b

2

+mh

)(

k

k−m

)

and that the distancew 2 between the centre line and the down-slope side is

w 2 =

(

b

2

+mh

)(

k

k+m

)

Show that the area of the cutting is

1

2 m

[(

b

2

+mh

)

(w 1 +w 2 )−

b^2

2

]