A cricket ball is hit vertically upwards so that its ...
A cricket ball is hit vertically upwards so that its height (in metres) at a given time (in seconds) is given by the formula: H = 20t - 5t^2, where H is the height of the ball. Sketch the graph of H = 20t - 5t^2 using sensible scales on both the horizontal and vertical axes. Use this graph to find the maximum height that the ball will reach. Use the graph to determine the time it will take for the ball to hit the ground.
Solution:
H = 20t - 5t^2
Where t is the time in seconds.
Domain should be [0, ∞) as time can’t be negative.
Vertex will be at t = -20/(2*(-5)) = -20/-10 = 2
H(2) = 20*2 – 5*2^2 = 40 – 20 = 20
Thus, vertex will be at (2, 20).
Since coefficient of x^2 is negative so parabola opens downwards.
Now let us find x and y-intercepts:
For finding y-intercepts, put t = 0.
H = 0
Thus, y-intercept is (0, 0).
For finding x-intercepts, put H = 0.
20t - 5t^2 = 0
5t(4 – t) = 0
Which gives t = 0, 4
Thus, x-intercepts are (0, 0) and (4, 0).
Using the above information, graph the function:
[pic]
Using the graph we can say that maximum height of the ball will be 20 meters and ball will reach the ground at t = 4 seconds.
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