Ball-height graph model

Ball-height graph model

Secondary 2
10 marks
TGM Original Questions

Optional extension

A ball’s height is \(y=18t-2t^2\) metres after \(t\) seconds.

  1. Complete the missing table values \(p,q,r\).[2]
  2. Draw the graph for \(0\le t\le9\).[2]
  3. Use it to find
    1. maximum height,[2]
    2. return time, and[2]
    3. times when height is \(32\) m.[2]
\(t\)\(0\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)
\(y\)\(0\)\(16\)\(p\)\(36\)\(40\)\(40\)\(q\)\(28\)\(r\)\(0\)

For graph readings, give values to the nearest 0.1 unit where an exact value cannot be read from the grid. Use the labelled axes and grid provided.

Solution:

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Answer:(a) \(p=28,q=36,r=16\) (c)(i) \(40.5\) m (ii) \(9\) s (iii) \(t\approx2.4,6.6\) s. (b) See the completed graph.

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