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Date None Specimen Marks available 7 Reference code SPNone.2.hl.TZ0.9
Level HL only Paper 2 Time zone TZ0
Command term Calculate Question number 9 Adapted from N/A

Question

A ladder of length 10 m on horizontal ground rests against a vertical wall. The bottom of the ladder is moved away from the wall at a constant speed of 0.5 ms1. Calculate the speed of descent of the top of the ladder when the bottom of the ladder is 4 m away from the wall.

Markscheme

let x, y (m) denote respectively the distance of the bottom of the ladder from the wall and the distance of the top of the ladder from the ground

then,

x2+y2=100     M1A1

2xdxdt+2ydydt=0     M1A1

when x=4, y=84 and dxdt=0.5     A1

substituting, 2×4×0.5+284dydt=0     A1

dydt=0.218 ms1     A1

(speed of descent is 0.218 ms1)

[7 marks]

Examiners report

[N/A]

Syllabus sections

Topic 6 - Core: Calculus » 6.2 » Related rates of change.

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