A ball is kicked off a cliff. The data in the table shows the quadratic motion of the ball until it first lands (no bounces).
The ball starts its motion at \(t=0\).
Determine
At \(t = 0\),
Height of the ball \(=\) Height of the cliff
Therefore, the height of the cliff is \(50\) metres.
The ball lands when its height is \(0\) metres.
The ball is in the air for \(5\) seconds.
The maximum height is a little over \(60\) m.
The ball reaches its maximum height at \(1.5\) s.
We need more information (an equation) to find the exact height.
The following quadratic data shows the fuel consumption of a car model Fibonauto for various speeds. Determine the most fuel efficient driving speed.
Fuel consumption
For instance, when travelling at \(60\) km/h the Fibonauto burns \(8.75\) litres of fuel to travel \(100\) km.
Thus, to find the most fuel efficient driving speed, we are trying to find the speed that minimizes the fuel consumption.
The data can be summarized in a graph as shown.
Since we are told in the question that this data is quadratic, we know the graph is a parabola. Thus, the curve is symmetric about the vertical line passing through the vertex of the parabola. Since the speeds of \(80\) km/h and \(100\) km/h have the same fuel consumptions, the axis of symmetry of the curve must lie halfway between these two points, at \(90\) km/h.
The most fuel efficient driving speed is \(90\) km/h.