Question

A ball is dropped from a height of a little over 5 feet, and the height is measured at small intervals. The table below shows the results.Time (seconds) Height (feet)0.00 5.2350.04 5.1600.08 5.0270.12 4.8510.16 4.6310.20 4.3570.24 4.0300.28 3.6550.32 3.2340.36 2.7690.40 2.2580.44 1.635(a) Use a graphing calculator or spreadsheet program to find a quadratic model that best fits this data, using time as t and height as Pt. Round each coefficient to two decimal places.Pt=(b) Based on this model, what height is expected after 0.30 seconds? Round your answer to two decimal places.feet(c) What height is expected after 0.52 seconds? Round your answer to two decimal places.feet(d) Which of the two previous predictions is likely to be more reliable?0.52 seconds0.30 seconds(e) When do you expect the height of the ball to be 1 foot? Round your answer to the nearest hundredth of a second.After seconds

Answer 1

a)

From the graph, the coefficient of a, b, and c are:

a = -15.19

b = -1.39

c = 5.24

`\begin{gathered} \text{The quadratic model is} \\ h=-15.19t^2\text{ - 1.39t + 5.24} \end{gathered}`

b)

To find the height after 0.30 seconds, you will substitute t = 0.30

`\begin{gathered} h\text{ = -15.19 }*0.3^2\text{ - 1.39 }*\text{ 0.3 + 5.24} \\ h\text{ = -1.3671 - 0.417 + 5.24} \\ h\text{ = 3.4559} \\ h\text{ = 3.46 feet} \end{gathered}`

c)

To find the height after 0.52 seconds, you will substitute t = 0.52

`\begin{gathered} h\text{ = -15.19 }*0.52^2\text{ - 1.39 }*\text{ 0.52 + 5.24} \\ h\text{ = -4.11 - 0.723 + 5.24} \\ \text{h = 0.417} \end{gathered}`

d)

0.30 seconds is more reliable.

e)

`\begin{gathered} h=1foot_{} \\ h=-15.19t^2\text{ }-\text{ 1.39t + 5.24} \\ 1=-15.19t^2\text{ - 1.39t + 5.24} \\ 15.19t^2\text{ + 1.39t + 1 - 5.24 = 0} \\ 15.19t^2\text{ + 1.39t - 4.24 = 0} \end{gathered}`

t = 0.48455

Final answer

t = 0.48 seconds