I think 22.3 is correct, both my friends who studied mechanics and I (who did a level physics) got the same results. Please do update me im really curious as how the answer is 18 x
I think I may know how your teacher arrives the "answer" of 18.8 m/s at Y.
I suggest that you attempt to understand the statements in physics instead of just the formula or equations to use.
Using conservation of energy and consider roller-coaster and Earth as the system.
PE at X + KE at X = PE at Y + KE at Y mghX+21mvX2=mghY+21mvY2 ---(1)
It can be simplified to
vY=2g(hX−hY)+vX2 ---(2)
If equation (2) is used, the answer would 22.3 m/s as shown below:
Your teacher's answer did not consider the speed at X. If the speed at X is zero, we would arrive 18.8 m/s for the speed at Y using equation (2) as shown below:
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But the question stated that the speed at X is 12 m/s, so your teacher answer is incorrect.
Similarly, we would arrive the speed at Z to be 9.9 m/s using equation (2) and consider the speed at X to be zero. Test it yourself.
It may be good that you inform your teacher privately.