Q14 · 2024 · Technology-activeSimple familiar6 marks
QUESTION 14 (6 marks)
A football coach offered a 12-day intensive training clinic. During the clinic, the height that each player could kick a football was monitored.
One player’s kick heights could be modelled by , , where is vertical height (m) and is the time (days) spent in training.
a)[1 mark]
Determine the initial height that the player could kick the ball.
b)[1 mark]
Determine the training time needed for the player to be able to kick the ball to a height of 7 m.
c)[2 marks]
Determine the overall improvement in kick height achieved by completing the clinic.
d)[1 mark]
Determine the rate of change in kick height when days.
e)[1 mark]
Determine the training time (as a decimal) when the rate of change in kick height is 0.09 m/day.
WORKED SOLUTION
6 marksQCAA guide · typeset solution
ANSWER
a) m; b) days; c) m; d) m/day; e) days.
Worked solution
a)
b) Solving gives
c) Initially the kick height was 6 m. At the end of the course, so the improvement is
d) Using the derivative,
e) Solving gives
correctly determines the initial height
correctly determines the time required
correctly determines the kick height at the end of the course
determines the overall kick height improvement
correctly determines the derivative value when
correctly determines the time as a decimal
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