At the county July 4th celebration, a firework is launched. The function h(t) = -16t^2 + 96t gives the height in feet of the firework, t seconds after it has been launched. Does it make sense to find h(-2) in the context of this situation? Why or why not?

Answer 1

In the context of the situation, the function \( h(t) = -16t^2 + 96t \) describes the height of the firework at time \( t \) seconds after it has been launched. Since \( t \) represents time after the launch, it cannot be negative.

Finding \( h(-2) \) would mean evaluating the height of the firework 2 seconds before it was launched, which does not make sense in this scenario. Time \( t \) is only defined for non-negative values (i.e., \( t \geq 0 \)).

Thus, it does not make sense to find \( h(-2) \) because negative time does not have a physical meaning in the context of this situation.