Date | November 2020 | Marks available | 3 | Reference code | 20N.2.SL.TZ0.S_8 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Find | Question number | S_8 | Adapted from | N/A |
Question
The following diagram shows a water wheel with centre and radius metres. Water flows into buckets, turning the wheel clockwise at a constant speed.
The height, metres, of the top of a bucket above the ground seconds after it passes through point is modelled by the function
, for .
A bucket moves around to point which is at a height of metres above the ground. It takes seconds for the top of this bucket to go from point to point .
The chord is metres, correct to three significant figures.
Find the height of point above the ground.
Calculate the number of seconds it takes for the water wheel to complete one rotation.
Hence find the number of rotations the water wheel makes in one hour.
Find .
Find .
Determine the rate of change of when the top of the bucket is at .
Markscheme
valid approach (M1)
eg
(metres) A1 N2
[2 marks]
valid approach to find the period (seen anywhere) (M1)
eg , attempt to find two consecutive max/min,
(seconds) (exact) A1 N2
[2 marks]
correct approach (A1)
eg rotations per minute
(rotations) A1 N2
[2 marks]
correct substitution into equation (accept the use of ) (A1)
eg
valid attempt to solve their equation (M1)
eg
A1 N3
[3 marks]
METHOD 1
evidence of choosing the cosine rule or sine rule (M1)
eg
correct working (A1)
eg
A1 N3
METHOD 2
attempt to find the half central angle (M1)
eg
correct working (A1)
eg
A1 N3
METHOD 3
valid approach to find fraction of period (M1)
eg
correct approach to find angle (A1)
eg
( using )
A1 N3
[3 marks]
recognizing rate of change is (M1)
eg
( from )
rate of change is A1 N2
( from )
[2 marks]