# A rollercoaster carriage of mass 100kg has 45kJ of Kinetic Energy at the lowest point of its ride. Ignoring air resistance and friction between the wheels and the tracks, what is the maximum height above this point it could reach? [Take g as 10m/s/s)

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[A useful tip: always start by drawing a diagram!!]

This question is asking you to apply conservation of energy, i.e. at the highest point it can reach above the lowest point, all of this Kinetic Energy will have been transferred to Gravitational Potential Energy. This requires use of the equations KE=GPE and GPE=mgh, where m is the mass (in kg), g is the acceleration due to gravity (in m/s/s) and h is the maximum height above the lowest point (in m). All units of energy must be in J for these equations to give the right answers.

To get the height, rearrange the equations to give h=KE/mg, or rather h=45000/(100x10)=45m

(Note: the question gave the energy in kJ, so the number had to be multiplied by 1000 to give it in J, which gave the height in m)

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