Assume the function $H(t)=-10 t^{2}+50 t+6$ models the fireball data as the height of the fireball in feet above the ground as a function of time in seconds.
Part of the game includes a laser that can explode fireballs. If the laser's path follows the function below, when will the laser explode the fireball? Use technology (Desmos or graphing calculator).
\[
L(t)=7.9 t-10.6
\]
Based on your answer from the previous question (\#5), explain the meaning of your ordered pair.
- Answer in a complete sentence.
- Be specific.
Answer
Final Answer: The laser will explode the fireball at approximately \(\boxed{4.57}\) seconds.
Step 1 ：The problem is asking when the height of the fireball, modeled by the function \(H(t)=-10 t^{2}+50 t+6\), will be equal to the height of the laser, modeled by the function \(L(t)=7.9 t-10.6\). This means we need to find the time \(t\) when \(H(t) = L(t)\).
Step 2 ：This can be solved by setting the two equations equal to each other and solving for \(t\).
Step 3 ：The solution to the equation gives two values for \(t\). However, since time cannot be negative in this context, we discard the negative value.
Step 4 ：Therefore, the laser will explode the fireball at approximately 4.57 seconds.
Step 5 ：Final Answer: The laser will explode the fireball at approximately \(\boxed{4.57}\) seconds.
