GATE-2018 (24) :Wyllie – Time average equation

GATE-2007

A dipping limestone bed with a true width of 5meters shows an apparent width of 10meters on a horizontal surface.

Q.84: Calculate the true dip of the limestone bed

A) 70°                      B) 50°                           C) 30°                   D)10°

Solution:

Apparent width ab= 10m

True width bc= 5m

bc= ab sinθ

true width = apparent width * sinθ

sinθ= bc /ab

sinθ= 5/10

        =1/2

Sinθ = sin 30⁰

Θ = 30⁰

 Q.85: At what horizontal distance (meters) form the exposed upper surface of the bed should a vertical drill hole be made so as the intersect the top of the bed at a depth of 100 meters?

A) 73.2                       B)173.2                  C)273.2                       D)373.2

Solution:

Vertical drill distance = 100m

angle (Θ) = 30⁰

Horizontal distance = ?

tan 30⁰ = 100 / X

X= 100 / tan 30⁰

  =100 / 0.578

 X = 173 m

Horizontal distance bd = 173 m