One gallon of gasoline represents a significant amount of energy.

a) How many days would one average person need to work to produce the same useful work contained in one gallon of gasoline? (Be sure to state your assumptions)
b) Josephine Bruin, who weighs 80 kg, has a motorcycle that weighs 100 kg that is equipped with a gasoline tank that holds 1 gallon of gas. Calculate how many times Josephine could use her motorcycle to climb from sea level to the top of Mt. Everest which is of 8,848 m above sea level on one tank of gas assuming that Josephine’s motorcycle is 100% efficient?
c) Josephine tries to use her motorcycle to actually climb from sea level to the top of Mt. Everest and she finds that she runs out of gas at an altitude of 6,000 m above sea level. Estimate the overall climbing efficiency of Josephine’s motorcycle.
d) Once Josephine runs out of gas at an altitude of 6,000 m above sea level, she decides to turn around and coast back down the mountain to sea level, using her brakes to control her speed. Calculate the breaking power (in Watts) that Josephine would need to apply to maintain a constant speed of 5 m/sec measured along the road, assuming that the road down the mountain is 10 km long and has a constant slope.

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.