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A man of mass 60 kg rides a scooter of mass 100 kg. He accelerates the scooter to a velocity v. The next day, his son with a mass of 40 kg joins him as a passenger. If the scooter reaches the same speed on both days in the same time interval, what is the ratio of the fuel of the tank used on the two days? Assume that the energy transfer to the scooter happens entirely due to fuel, and no other losses occur due to air resistance and friction.
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Day 1 mass \(= 60 + 100 = 160\ \text{kg}\); Day 2 mass \(= 60 + 100 + 40 = 200\ \text{kg}\).
Fuel \(\propto\) kinetic energy \(= \tfrac{1}{2}mv^2\), and \(v\) is the same, so fuel \(\propto\) mass.
Ratio (Day 1 : Day 2) \(= 160 : 200 = \mathbf{4 : 5}\).
