Question

The displacement function of a rock thrown straight up in the air is given by f(t)= -2t^2 + 15.7t meters, where t is measured in seconds find the total distance traveled by the rock when it reaches the ground a. 30.81 mb. 31.40 mc. 61.62 md. 92.43 m

Answer 1

As the rick is thrown straight up in the air and the function of its displacement is quadratic it means that the rock traveled a distance up to its maximum and then down to the ground. Then, the function value in the maximum is half the distance traveled by the rock.

$f(t)=-2t^2+15.7t$

Use the next formula to find the time (t) in the maximum point of quadratic function:

$\begin{gathered} f(x)=ax^2+bx+c \\ \\ x_{max}=-\frac{b}{2a} \end{gathered}$$t_{max}=-\frac{15.7}{2(-2)}=-\frac{15.7}{-4}=3.925$

Evaluate the function for t=3.925 to find the maximum value:

$\begin{gathered} f(3.925)=-2(3.925)^2+15.7(3.925) \\ f(3.925)\approx-2(15.4056)+61.6225 \\ f(3.925)\approx-30.8112+61.6225 \\ f(3.925)\approx30.8113 \end{gathered}$

Multiply the maximum value by 2 to get the total distance traveled by the rock:

$30.8113*2\approx61.62$Then, the total distance traveled by the rock when it reaches the ground is 61.62metersAnswer: C