Parabola Application: Dive Trajectory Calculation

Exploring the Dive Trajectory Function

The function h(t) = -4t^2 + 11t + 3 describes the height of a diver above the water in meters at different time intervals t seconds after leaving the springboard. By analyzing this function, we can determine various key points during the dive.

Finding Specific Heights and Times

a. What is the height of the springboard? The springboard's height can be found by evaluating h(0). Plugging in t = 0 gives us h(0) = -4(0)^2 + 11(0) + 3 = 3 meters.

b. When does the diver hit the water? The diver hits the water when h(t) = 0. Solving -4t^2 + 11t + 3 = 0, we get t = 3 seconds.

c. At what time is the diver at the same height as the springboard during descent? We solve h(t) = 3 to find t = 0 (start) and t = 2.5 seconds (during descent).

d. When does the diver reach the peak of the dive? The peak occurs at t = -b/(2a) = -11/(2*-4) = 1.375 seconds.