Question

a gannet is a type of seabird that dives into the water to catch fish. some gannets have been observed diving at speeds of more than 60 miles per hour! this function models the height of a gannet, in feet, t seconds after starting its dive:
$f(t) = -16(t - 1.7)(t + 1.7)$
complete the sentence.
the gannet strikes the water \boxed{} seconds after starting its dive.

Explanation:

Step1: Understand the problem

We need to find the time \( t \) when the gannet strikes the water, which means the height \( f(t) = 0 \) (since height is 0 when it's in the water). So we set the function \( f(t)=- 16(t - 1.7)(t + 1.7)=0 \) and solve for \( t \).

Step2: Solve the equation

Since \( - 16
eq0 \), we can set each factor equal to zero:

• For \( t - 1.7=0 \), we get \( t = 1.7 \).
• For \( t + 1.7=0 \), we get \( t=-1.7 \).

But time \( t \) cannot be negative in this context (we are talking about time after starting the dive), so we discard \( t = - 1.7 \).

Answer:

\( 1.7 \)