Question

When a ball is thrown the model of its path is y = ax 2 + bx + c.

y is the vertical height in metres of the ball above the horizontal ground. x is the horizontal distance in metres that the ball has travelled from where it was thrown. a, b and c are constants.

1 (a) A ball is thrown from (0, 0). The model of the ball’s path is y = _ 8 1 x 2 + 4 5 x.

(i) On the diagram, sketch the graph of this equation for 0 Y x Y 12.


(ii) How far does the ball travel horizontally before hitting the ground? .............................................

(iii) What is the greatest height that the ball reaches? .............................................

(iv) A vertical fence, 2m high, stands on the horizontal ground 6m from where the ball was thrown. How far above this fence is the ball when it is 6m from where it was thrown? .............................................

(v) There are two positions where a 2m high fence could be built so that the ball just passes over the top. One position is 2m from where the ball was thrown. Find the other position. .............................................
(b) The ball is now thrown from 1.5m above the ground. Use this information to modify the model in part (a). ..................................................................

A second ball is thrown from (0, 0). It passes through the points (3, 1.2) and (5, 0). (a) Use these co-ordinates to write down three equations in a, b and c.

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(b) Solve your equations to find values for a, b and c, and write down the equation of the path of this second ball.
a = ...........................................
b = ...........................................
c = ...........................................

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(c) A vertical fence, 2m high, stands on the horizontal ground 2m from where this second ball was thrown. Will this second ball hit the fence? Explain your answer. .................................................................................................................................................................... ....................................................................................................................................................................

Answer 1

Answer:

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