Why square the wave height instead of using it directly?

Energy grows with the square of the amplitude of water particle motion, so double the height means four times the energy.

Both a wave-cut platform and a beach are flat, so how do you tell them apart?

The platform is bare rock at the cliff foot and is erosional, while a beach is loose sediment and depositional.

S5 Geography | Coastal Landforms Paper 1 (Foundation)

2026-11-04

Tutor Prep Guide · Secondary Geography

This paper does one thing: it fixes the core numerical relations of coastal erosion and deposition, with wave energy following the square of wave height and platform width following how far the cliff has retreated.

Attempt first, mark afterwards　Allow about twenty minutes; write the formula and the unit first, check whether the denominator is years or distance, then compare with the answers.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 items
Suggested time	About 20 minutes
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S5 Geography \| Coastal Landforms
Level	S5 (Secondary 5) Geography

02　Questions (10 items)

FoundationTwo wave sets have heights of 1.5 m and 3 m. If wave energy is proportional to the square of wave height, how many times more energy does the second set carry?
FoundationA cliff retreats 24 m in 60 years. What is the average retreat per year, and how far will it retreat in the next 30 years at that rate?
FoundationA cliff retreats 0.5 m a year and a wave-cut platform has been developing at its foot for 40 years. Roughly how wide is the platform?
FoundationLongshore drift moves 6,000 cubic metres of sediment a year. How much moves in 10 years, and how much piles up on one side of a groyne in 5 years if it traps everything?
IntermediateA sea stack is 18 m high and the sea removes 0.3 m a year. How many years before it is lower than 6 m and becomes a stump?
IntermediateA sea wall costs 48,000,000 dollars, lasts 40 years, needs 300,000 dollars of maintenance a year and protects assets worth 96,000,000 dollars. What is the total cost and the benefit-cost ratio?
IntermediateA beach 800 m long and 40 m wide is nourished to a width of 60 m with sand 1.5 m deep at 25 dollars a cubic metre. How much sand is needed and what does it cost?
ChallengeA coast receives 8,000 cubic metres of sediment a year from rivers, loses 3,000 offshore and is dredged for 2,500. What is the net sediment budget, and what happens if dredging rises to 6,000?
ChallengeA house stands 12 m from a cliff edge that retreats 0.8 m a year. When will the edge reach the house, and is that figure a lower or an upper bound?
Error redoA student writes that a wave-cut platform is sediment deposited at the foot of a cliff. Is that right, and if the cliff retreats 0.6 m a year, how wide a platform forms in 50 years?

03　Answers and one-line notes

#	Answer	One-line note
1	4 times.	The ratio is 3 over 1.5, squared, which is two squared, or 4; doubling height quadruples energy, so storm waves erode far harder than calm ones.
2	0.4 m a year, so 12 m in 30 years.	24 divided by 60 gives 0.4 m a year, and times 30 gives 12 m; the rate is total retreat over total years.
3	About 20 m.	0.5 times 40 gives 20 m; a wave-cut platform is the rock surface left behind as the cliff retreats, so the further the cliff has gone, the wider it is.
4	60,000 cubic metres in 10 years, and 30,000 cubic metres in 5 years.	6,000 times 10 gives 60,000, and times 5 gives 30,000; a groyne does not remove sediment, it piles it on one side and starves the other.
5	About 40 years.	The sea must remove 18 less 6, or 12 m; dividing by 0.3 gives 40 years. A stack is what remains after an arch collapses, and further erosion reduces it to a stump.
6	Total cost 60,000,000 dollars and a ratio of 1.6.	Maintenance over the life is 300,000 times 40, or 12,000,000, so the total is 60,000,000; dividing assets by that gives 1.6, and only a ratio above one justifies the wall.
7	24,000 cubic metres costing 600,000 dollars.	The width gained is 60 less 40, or 20 m; the volume is 800 times 20 times 1.5, or 24,000 cubic metres, and times 25 gives 600,000 dollars.
8	A net gain of 2,500 cubic metres a year, turning into a net loss of 1,000 at the higher dredging rate.	8,000 less 3,000 less 2,500 leaves 2,500; at 6,000 the same sum is -1,000, a loss of 1,000 cubic metres a year, so the beach keeps narrowing.
9	15 years, and it is only a lower bound.	12 divided by 0.8 gives 15 years; an average rate hides occasional large collapses, so the real risk arrives earlier and a setback line needs extra margin.
10	Wrong: the platform is exposed rock left as the cliff retreats, so 30 m in 50 years.	0.6 times 50 gives 30 m; depositional features are beaches, spits and bars, whereas a wave-cut platform is erosional and only appears after the cliff has moved back.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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