A tennis ball of mass 350 g is thrown vertically upwards at a speed of 4 m/s. If M is the maximum gravitational potential energy of the ball and H is the maximum height it reaches, then which one of the following is correct? (Take g = 10 m/s²)
- A.M = 5·6 J, H = 1·6 m
- B.M = 2·8 J, H = 1·6 m
- C.M = 5·6 J, H = 0·8 m
- D.M = 2·8 J, H = 0·8 m
Correct answer
Explanation
The correct answer is D, M = 2·8 J, H = 0·8 m. At the top of its flight all the kinetic energy of the ball has turned into gravitational potential energy.
The mass is 350 g, that is 0·35 kg. Its kinetic energy at launch is ½mv² = ½ × 0·35 × 4 × 4 = 2·8 J, so the maximum potential energy M is also 2·8 J (air resistance is ignored). The height follows from mgH = 2·8 J, or more simply from H = v²/2g = 16/20 = 0·8 m. Note that the height does not depend on the mass at all.
A is wrong: 5·6 J comes from forgetting the ½ in the kinetic energy, and 1·6 m from using v²/g.
B is wrong: the energy is right but the height is doubled by dropping the 2 in v²/2g.
C is wrong: the height is right but the energy is doubled.
Exam tip: for a body thrown straight up, H = u²/2g and the energy at the top equals ½mu²; always convert grams to kilograms first.
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