Please help me out in answering this question thank you. **Designing a Roller Coaster: Energy Considerations**You're tasked with the exciting challenge of designing a roller coaster for the Happy Land Safari and Fun Complex. The focus is on the final section of the ride, where a 200 kg cart will hit the bottom of a 10-meter-tall hill at a speed of 11 m/s. Engineers have installed speed boosters to ensure the cart ascends the hill successfully. Your objective is to determine the amount of work that the speed boosters should perform on the cart to ensure it reaches the top.Options to consider:- The speed boosters need to do at least 7,500 J of work to the cart.- The speed boosters need to do at least 12,100 J of work to the cart.- The speed boosters do not need to do any work to the cart. *(Selected Option)*- The speed boosters need to do at least 19,600 J of work to the cart.**Understanding the Options:** Each option suggests a distinct amount of work needed by the speed boosters, measured in joules (J), to help the cart make it to the top of the hill. The correct choice depends on the calculation of kinetic and potential energy involved in the ride's motion.

In this problem we will use the concept conservation of energy. For the roller coaster to reach the top of the hill, the kinetic energy of coaster at bottom of hill must be equal to its potential energy at the top of the hill. If kinetic energy is more than the potential energy than speed boosters does not need to do any work. But if kinetic energy is less than the potential energy than the speed boosters need to do the work equal to the difference of potential energy at top and kinetic energy at bottom. Given m=200 Kg (mass of roller coaster) v=11m/s (speed of roller coaster at bottom of hill) h=10 m (height of hill) Now kinetic energy at bottom of hill is given by K.E=12mv2=12×200×112=12100 J The potential energy at top of hill is given by P.E=mghg=9.8m/s2P.E=200×9.8×10=19600JFrom above we see that P.E>K.E hence the speed boosters need to do work which is given by W=P.E-K.EW=19600-12100=7500J