Answer:
2.75 seconds
Explanation:
we are asking nothing else than after how many seconds (after jumping) is the diver at the same height above the water as in his starting position before jumping ?
that is a key factor to understand it that way, because that allows us to calculate the starting point for t=0.
-4t² + 11t + 3 = h(t)
so, for t = 0
h(0) = -4×0² + 11×0 + 3 = 3
so, what do you know, the springboard is actually 3 meters above the water - a 3m springboard.
now, we want to solve this for t under the constriction that the result must be 3. for what values of t is that the case ?
one we know already (t = 0). but there must be a second one (based on the scenario and also on the fact that this is a squared equation).
3 = -4t² + 11t + 3
0 = -4t² + 11t = t×(-4t + 11)
so, we see, t = 0 is one possibility. that was the starting position.
the other one is, when (-4t + 11) = 0.
-4t + 11 = 0
11 = 4t
t = 11/4 = 2.75 seconds.
=>
2.75 seconds after jumping up then falling back down is the diver back at the same height above the water as the diving board.