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 ms−1. 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+2√84dydt=0 A1
dydt=−0.218 ms−1 A1
(speed of descent is 0.218 ms−1)
[7 marks]