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Group A—Continued Group B—Continued
5. The steepness of a slope is expressed in units of percent when 5. A field on a farm is 326 m wide. The elevation of the field is 39 m
one is studying mass wasting. Geologists investigating a landslide at the uphill edge and 33 m at the downhill edge. What is the
surveyed the elevation of a hillside and found it to be 823 m at slope of this field in percent?
the bottom and 956 m at the top. The survey points were 452 m
apart from each other. How steep is this hillside in percent?
6. One factor that controls mass wasting is relief. Relief is the 6. An exposed batholith has a summit elevation of 556 m and a
difference in elevation between the highest and lowest points on base elevation of 420 m. What is the relief of this batholith?
a landscape. An extinct volcano has a summit elevation of
5,930 m above a relatively flat landscape with an average
elevation of 5,400 m. What is the relief of this volcano?
7. The gradient of a streambed is determined by taking the 7. The elevation of a streambed is surveyed near a bridge to be
elevation at two places along the stream, measuring the distance 2,367 m. At another bridge 12.2 km downstream the elevation is
between these points, and applying the slope equation. Stream 2,232 m. What is the gradient of this stream?
gradient is usually stated in units of meters per kilometer or feet
per mile. What is the gradient of a stream that has an elevation
change of 5 m over a distance of 13.8 km?
8. Each year, sheet erosion removes 1 mm of soil from a drainage 8. Each year, sheet erosion removes 0.9 mm of soil from a cornfield
2
4
2
2
basin that has an area of 5.12 × 10 km . The average density of that has an area of 4.1 × 10 m . The average density of the soil
3
3
the soil being eroded in the drainage basin is 1.35 Mg/m . What being eroded from the field is 1.35 Mg/m . What is the annual
is the annual sediment load, in Mg, transported by the stream in sediment load, in Mg, being introduced to the stream in this
this drainage basin? drainage basin?
2
3
9. A river that has been dammed transports 1.6 × 10 Mg/yr of 9. A river that has been dammed transports 1.1 × 10 Mg/yr of
sediment to a symmetrical delta that is 150 km long and has sediment to a symmetrical delta that is 120 km long and has
240 km of coastline. Assume the delta is an isosceles triangle and 100 km of coastline. Assume the delta is an isosceles triangle
the sediment from the river is deposited on the topset beds. The and the sediment from the river is deposited on the topset
3
3
density of the sediment is 1.2 Mg/m . What is the thickness beds. The density of the sediment is 1.2 Mg/m . What is the
(z) of sediment deposited on the topset beds of the delta in thickness (z) of sediment deposited on the topset beds of the
1,000 years? delta each year?
10. Before the river in exercise 9 was dammed, the river 10. Before the river in exercise 9 was dammed, the river
5
6
transported 4.5 × 10 Mg of sediment each year. What is the transported 2.1 × 10 Mg of sediment each year. What is the
thickness (z) of sediment deposited on the topset beds of the thickness (z) of sediment deposited on the topset beds of the
delta in 1,000 years? delta each year?
11. The discharge (Q) of a stream is the velocity (v) times the 11. The discharge (Q) of a stream is the velocity (v) times the
cross-sectional area (A): Q = vA. What is the discharge of a cross-sectional area (A): Q = vA. What is the discharge of a
stream with a velocity of 2.6 m/s and a cross-sectional area of stream with a velocity of 1.73 m/s and a cross-sectional area of
2
2
3
54.8 m ? 1.72 × 10 m ?
12. What is the velocity (v) of a stream with a discharge (Q) of 12. What is the velocity (v) of a stream with a discharge (Q) of
3
3
3
3
2
3
2
3
1.13 × 10 m /s and a cross-sectional area (A) of 3.68 × 10 m ? 8.53 × 10 m /s and a cross-sectional area (A) of 5.27 × 10 m ?
13. Glacial end moraines record the position of the ice terminus at a 13. Glacial end moraines record the position of the ice terminus at a
given time. As climate warms, the rate of glacial retreat can be given time. As climate warms, the rate of glacial retreat can be
determined by dividing the distance between end moraines by determined by dividing the distance between end moraines by
the amount of time required for the glacier to retreat that the amount of time required for the glacier to retreat that
distance. An end moraine from 2007 is located 0.96 km distance. An end moraine from 2001 is located 2.47 km
upvalley from the position from 1933. What is the rate of upvalley from the position from 1893. What is the rate of
glacial retreat? glacial retreat?
14. A 2002 survey of glacial end moraines indicated a 1.2 km long 14. A 1998 survey of glacial end moraines indicated a 0.65 km long
−2
−2
glacier was retreating at a rate of 1.25 × 10 km/yr. At this rate glacier was retreating at a rate of 1.43 × 10 km/yr. At this rate
of retreat, in what year will the glacier disappear? of retreat, in what year will the glacier disappear?
15. Rates of tectonic uplift can be determined from the age and 15. Rates of tectonic uplift can be determined from the age and
elevation of stream terraces, flat-surfaced deposits of streambed elevation of stream terraces, flat-surfaced deposits of streambed
sediment that represent ancient floodplains. By dating the age of sediment that represent ancient floodplains. By dating the age of
the terraces and measuring the elevation of the terrace, the uplift the terraces and measuring the elevation of the terrace, the uplift
rate is the difference in elevation of the terraces divided by the rate is the difference in elevation of the terraces divided by the
difference in ages of the terraces. A terrace at 393 m elevation is difference in ages of the terraces. A terrace at 164 m elevation is
12,500 years old while the current floodplain is 379 m. What is 101,000 years old while another terrace at 111 m is 24,800 years
the rate of uplift in mm/yr? old. What is the rate of uplift in mm/yr?
520 CHAPTER 20 Shaping Earth’s Surface 20-20