Question 22M.2.SL.TZ2.d
| Date | May 2022 | Marks available | [Maximum mark: 2] | Reference code | 22M.2.SL.TZ2.d |
| Level | SL | Paper | 2 | Time zone | TZ2 |
| Command term | Calculate | Question number | d | 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.
In a test the airboat is tied to the river bank with a rope normal to the bank. The fan propels the air at its maximum speed. There is no wind.
The rope is untied and the airboat moves away from the bank. The variation with time t of the speed v of the airboat is shown for the motion.
The fan is rotating at 120 revolutions every minute. Calculate the centripetal acceleration of the tip of a fan blade.
[2]
ALTERNATE 1
« ω = » 4 rad s−1 ✓
« a = r ω2= » 280 « m s−2 » ✓
ALTERNATE 2
« » = 22.6 m s−1 ✓
« »= 280 « m s−2 » ✓
Allow ECF from MP1 for wrong ω (120 gives 2.6 x 104 « m s−2 »)
Allow ECF from MP1 for wrong T (2 s gives 18 « m s−2 »)
