Consider a rock mass that fails on a mountainside at an elevation of 2300 metres

ID: 1592877 • Letter: C

Question

Consider a rock mass that fails on a mountainside at an elevation of 2300 metres. This rock

mass crashes onto the valley floor at an elevation of 1600 metres and comes to an abrupt halt

on the opposite valley wall at an elevation of 1800 metres. Calculate the maximum velocity

(in km/hr) at which the rock mass was moving when it first arrived on the valley floor.

Calculate the minimum velocity (in km/hr) the rock mass was travelling as it began its ascent

up the opposite valley wall.

The rock mass travelled for a distance of 3 kilometres as it crossed the valley floor. Given

the range of rock mass velocities, compute how much time citizens living on the valley floor

would have to get out of the path of this rapidly moving rock mass if they were fortunate

enough to have witnessed the initial rock failure.

v = d/t ; where d = 3 km

using equation

v^2 = u^2 + 2as

v^2 = 0 + 2*9.81*2300

v = 212.4 m/s

v = 212.4 *(3600 / 1000) = 764.7 kph (maximum velocity)

now for minimum velocity

by the conservation of energy

PE gain = remaining KE after impact

mgh = (1/2)*mv^2

gh = (1/2)*v^2

9.81*(1800 - 1600) = 0.5*v^2

v^2 = 3924

v = 62.64 m/s = 225.5 kph

2)

Using equation

s = 1/2 (u+v)t

Average velocity as it moves across the valley = (62.64 + 0) /2 = 31.32 m/s

Time taken = distance / velocity = 3000 / 31.32 = 95.8 seconds

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