Answer:
The time it will take Jake to hit the water ia approximately 4.46 seconds
Step-by-step explanation:
The given parameters in the question are; feet
The height off the ground, of the diving board from which Jake dives, h₀ = 18 feet
g = The acceleration due to gravity
The maximum height Jake reaches, h = 26 feet
The time Jake takes to reach maximum height = 2 seconds
We have;
h = h₀ + u·t + 1/2·g·t²
v² = u² - 2·g·(h - h₀)
v = u - gt
u = gt
Where;
v = The final velocity
u = The initial velocity
t = The time taken
u = 9.81 × 2 = 19.62 m/s
The vertex form of a quadratic equation is f(x) = a(x - h)² + k², with the vertex = (h, k)
Substituting the values, gives;
26 = 18 + u·t - 1/2 × 9.81 × t²
8 = 19.62·t - 1/2 × 9.81 × t² = 19.62·t - 4.905·t²
19.62·t - 4.905·t² - 8 = 0
Therefore, the standard form is -4.905·t² + 19.62·t - 8 = 0
The coordinate of the vertex, is (2, 8), the vertex form is therefore;
-4.905(t - 2)² + 8
2) The time it will take Jake to hit the water is given as follows;
The height at which Jake meets the water = -18 feet from initial height
∴ -4.905·t² + 19.62·t - 8 = -18
-4.905·t² + 19.62·t - 8 + 18 = 0
-4.905·t² + 19.62·t + 10 = 0
t² - 4·t - 2.04 = 0
By the quadratic formula, we have;
t = (4 ± √((-4)² - 4 × 1 × -2.04))/(2×1)
t ≈ 4.46 seconds or t ≈ -0.46 seconds
∴ t ≈ 4.46 seconds
The time it will take Jake to hit the water ≈ 4.46 seconds.
