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On another planet, a ball is launched vertically into the air from the ground - HSC - SSCE Mathematics Standard - Question 20 - 2023 - Paper 1
Question 20
On another planet, a ball is launched vertically into the air from the ground. The height above the ground, h metres, can be modelled using the function h = -6t² +... show full transcript
Worked Solution & Example Answer:On another planet, a ball is launched vertically into the air from the ground - HSC - SSCE Mathematics Standard - Question 20 - 2023 - Paper 1
Step 1
Based on the graph, what is the maximum height reached by the ball?
Answer
The maximum height reached by the ball can be identified from the graph as the peak point. Analyzing the graph, the highest point on the vertical axis corresponds to 24 metres. Therefore, the maximum height is:
Maximum height = 24 m
Step 2
Based on the graph, at what TWO times is the ball at $ rac{3}{4}$ of its maximum height?
Answer
First, we calculate rac{3}{4} of the maximum height:
rac{3}{4} imes 24 = 18 ext{ m}
Next, we examine the graph to determine at what two instances the height is 18 m. From the graph, it is observed that the ball reaches this height at:
1 second and 3 seconds.