Question

you jump off the end of a ski jump. your height in meters relative to the height of the ski jump after t seconds is given by $h(t)=-5t^{2}+12t$. how high will you be after 2 seconds? at this point are you going up or coming down? a you are 6 meters above the ski jump height and you are coming down. b you are 4 meters above the ski jump height and you are coming down. c you are 7 meters above the ski jump height and you are coming down. d you are 2 meters above the ski jump height and you are coming down.

Explanation:

Step1: Calculate height at t = 2

Substitute \(t = 2\) into \(h(t)=- 5t^{2}+12t\).
\[

$$\begin{align*} h(2)&=-5\times(2)^{2}+12\times2\\ &=-5\times4 + 24\\ &=-20 + 24\\ &=4 \end{align*}$$

\]

Step2: Determine if going up or down

Find the derivative of \(h(t)\), \(h^\prime(t)=-10t + 12\).
Substitute \(t = 2\) into \(h^\prime(t)\):
\[

$$\begin{align*} h^\prime(2)&=-10\times2+12\\ &=-20 + 12\\ &=-8 \end{align*}$$

\]
Since \(h^\prime(2)<0\), the height is decreasing, so coming down.

Answer:

B. You are 4 meters above the ski jump height and you are coming down.