Final answer:
When driving a truck with a manual transmission down a steep hill, use the same gear you would use to climb the hill for engine braking and control. In scenarios involving coasting down or up hills, energy conversions between potential and kinetic energy, as well as losses due to friction, determine the outcomes.
Step-by-step explanation:
Understanding Gearing and Slopes in Manual Transmission Trucks
When driving a new truck with a manual transmission down a long, steep downhill grade, you will probably have to use the same gear you'd use to climb the hill. This is to maintain control and to use engine braking to help slow down the vehicle. Using the same gear offers a level of resistance that prevents the truck from speeding uncontrollably downhill.
When referring to the provided scenarios, the maximum velocity that a truck can achieve at the bottom of a hill when coasting freely is determined by gravitational potential energy conversion into kinetic energy. However, in reality, the truck will not achieve this velocity due to air resistance and rolling resistance. Similarly, a car would potentially coast up the height determined by its initial kinetic energy if there is no friction, but again, frictional forces will convert some of that energy into thermal energy, thus reducing the height it can actually reach.
When discussing the force of friction for a car coasting up a hill, one must calculate the energy lost to heat due to friction and then determine the average force based on this energy loss and the distance covered. The energy types involved in the scenario where the car coasts after running out of gasoline involve conversions between potential energy, kinetic energy, and energy lost to friction.