You have been hired to design a safety system to protect drivers going down hills during an ice storm. The planned system consists of a bumper, which can be considered a stiff spring, at the bottom of the hill. In the scenario you are given, the car starts from rest at the top of a hill which makes an angle T with the horizontal. The distance that the car slides from the top of the hill until it is stopped by the spring is L. For the worst case scenario, assume that there is no frictional force between the car and road due to the ice. If the maximum compression of the spring from its equilibrium position is D, your job is to find out the required spring constant k in terms of D, L and T.