Designing a wheelchair ramp within a gradient limit
Designing a wheelchair ramp within a gradient limit
IP 2
9 marks
A guideline states that a wheelchair ramp may rise at most \(1\) m for every \(12\) m of horizontal distance.
- Find the greatest angle that a ramp may make with the horizontal.[2]
- A ramp must rise \(0.75\) m. Find the least horizontal distance it needs and the corresponding length of the ramp surface.[3]
- Only \(4\) m of horizontal space is available, so the ramp is built as a zig-zag of equal straight sections joined by level landings, each section using at most \(4\) m of horizontal space. Find the least number of sections. Explain why the total length of sloping surface is the same as in (b).[4]
Solution:
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Answer:(a) \(4.76^\circ\) (b) \(9\) m horizontally, ramp \(9.03\) m (c) \(3\) sections; same gradient throughout, so total sloping length \(=9\sqrt{1+\left(\dfrac{1}{12}\right)^2}\approx9.03\) m
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