Final answer:
When passengers feel 50% heavier on a roller coaster, the centripetal force acting on them is 1.5 times their true weight, as they experience their normal true weight plus an additional half due to the centripetal force. Therefore the correct answer is b. 1.5 times their true weight.
Step-by-step explanation:
The question is asking what the centripetal force acting on the passengers is when they feel 50% heavier than their true weight as the roller coaster car goes through a dip with a 30 m radius of curvature.
We know that the normal force on the passengers in circular motion is equal to the centripetal force required to keep them moving in a circle.
When the passengers feel 50% heavier, this implies that the centripetal force is providing an additional force equal to half their weight. Therefore, the total force they feel would be their true weight (the gravitational force) plus half again as much.
Mathematically, if W is the true weight, the passengers feel a force of W + (0.5 x W) = 1.5W. The centripetal force would need to be this additional 0.5W in order to make this happen. Thus the correct answer is that the centripetal force is 1.5 times their true weight.