Question

During heavy rain, a section of a mountainside measuring 5.1 km horizontally (perpendicular to the slope), 1.5 km up along the slope, and 1.6 m deep slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a surface area of the valley measuring 0.57 km x 0.57 km and that the mass of a cubic meter of mud is 1900 kg. What is the mass of the mud sitting above a 5.9 m2 area of the valley floor?

Answer 1

V = Volume of the mud

Volume of mud is given as

V = 5100 x 1500 x 1.6

V = 1.224 x 10⁷ m³

A_v = area of the valley = 570 x 570 = 324900 m²

h = height of mud in the valley

Volume remains same

hence

V = A_v h

1.224 x 10⁷ = (324900) h

h = 37.7 m

A_f = area of the valley floor = 5.9 m²

$\rho$ = density of mud = 1900 kg/m³

mass of mud is given as

m = $\rho$ A_f h

m = 1900 x 5.9 x 37.7

m = 422617 kg