A $1200kg$ roller coaster car is released from rest at the top of a $90m$ tall hill. As it travels down the hill, $250kJ$ of energy are dissipated as heat. Following the hill is a vertical loop of height $h.$ The car's speed at the top of the loop cannot be less than half the speed the car has at the bottom of the hill. What is the maximum height of the loop? Dissipation is negligible after the car has reached the bottom of the hill, and as it goes around the loop.