Question 22M.2.HL.TZ2.a
| Date | May 2022 | Marks available | [Maximum mark: 3] | Reference code | 22M.2.HL.TZ2.a |
| Level | HL | Paper | 2 | Time zone | TZ2 |
| Command term | Outline | Question number | a | Adapted from | N/A |
Airboats are used for transport across a river. To move the boat forward, air is propelled from the back of the boat by a fan blade.
An airboat has a fan blade of radius 1.8 m. This fan can propel air with a maximum speed relative to the boat of 20 m s−1. The density of air is 1.2 kg m−3.
Outline why a force acts on the airboat due to the fan blade.
[3]
ALTERNATIVE 1
there is a force «by the fan» on the air / air is accelerated «to the rear» ✓
by Newton 3 ✓
there is an «equal and» opposite force on the boat ✓
ALTERNATIVE 2
air gains momentum «backward» ✓
by conservation of momentum / force is rate of change in momentum ✓
boat gains momentum in the opposite direction ✓
Accept a reference to Newton’s third law, e.g. N’3, or any correct statement of it for MP2 in ALT 1.
Allow any reasonable choice of object where the force of the air is acting on, e.g., fan or blades.
The majority succeeded in making use of Newton's third law to explain the force on the boat. The question was quite well answered but sequencing of answers was not always ideal. There were some confusions about the air hitting the bank and bouncing off to hit the boat. A small number thought that the wind blowing the fan caused the force on the boat.
bi) This was generally well answered with candidates either starting from the wind turbine formula given in the data booklet or with the mass of the air being found using .
1bii) Well answered by most candidates. Some creative work to end up with 240 was found in scripts.
1ci) Many candidates gained credit here for recognising that the resistive force eventually equalled the drag force and most were able to go on to link this to e.g. zero acceleration. Some had not read the question properly and assumed that the rope was still tied. There was one group of answers that stated something along the lines of "as there is no rope there is nothing to stop the boat so it can go at max speed.
1cii) A slight majority did not realise that they had to find the area under the velocity-time graph, trying equations of motion for non-linear acceleration. Those that attempted to calculate the area under the graph always succeeded in answering within the range.
1ciii) Use of the average gradient was common here for the acceleration. However, there also were answers that attempted to calculate the mass via a kinetic energy calculation that made all sorts of incorrect assumptions. Use of average acceleration taken from the gradient of the secant was also common.
