I am new here. I need a bit of help. Not the best at math.
Johnny jumps from a plane at $3000$ feet in the sky. After $35$ seconds, he deploys a parachute. $h =$ height. $t =$ # of seconds after jumping. $$h(t) = \begin{cases} -51.5t + 3000 & \text{if $0 \leq t \leq 35$}\\ -8.9t + 1509 & \text{if $t > 35$} \end{cases} $$ When does Johnny hit the ground?
I thought a process of $3000 = -8.9t + 1509$ would work but when I solved for $t$, my results were $-167.53$.
I like to picture this on an $x,y$ plane and I do not understand how a negative number could be incorporated in this context. Or perhaps my answer is just wrong altogether?
Also for clarification, what in this sense would be an example of functional notation?
I assume the explanation would provide the interval notation. I think it would be $(-167.53, 3000)$?
Answer
He jumps at $0$, so the function must be set to $0$. \begin{align*} 0 & = -8.9t + 1509\\ 8.9t & = 1509\\ t &= 169.55 \end{align*} He lands a little over $2$ minutes.