Answer the whole of this question on a sheet of graph paper. A ball is thrown from the top of a buil

Question

Answer the whole of this question on a sheet of graph paper. A ball is thrown from the top of a building. Its vertical height $h$, in metres, above the ground at time $t$seconds during the flight is represented by the equation $h=20+5t-{{t}^{2}}$. Some corresponding values of $t$ and $h$ are given in the table given. $t$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $h$ $20$ $24$ $26$ $p$ $24$ $20$ $14$ $6$ Calculate the value of $p$. Using a scale of 2 cm to represent 1 unit, draw a horizontal $t$-axis for $0\le t\le 8$. Using a scale of 1 cm to represent 2 unit, draw a vertical $h$-axis for $0\le h\le 30$. On your axes, plot the points given in the table and join them with a smooth curve. Use your graph to estimate the maximum height of the ball from the ground, time when the ball is 18 m above the ground. Explain how you can use your graph to estimate the time when the ball hits the ground.

Accepted Answer

(a) $p=26$ (b) Graph shown in working (c)(i) Approximately $26.3$ m (ii) Approximately $5.37$ s (d) Extend the curve to $h=0$ and read $t\approx7.62$ s.

Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically

Quadratic Functions, Equations and Inequalities - Solving Quadratic Equations Graphically

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