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Jake dives from a diving board that is 18 feet off the ground. He reaches a maximum height of 26 feet after 2 seconds. What is the standard and vertex formula of this quadratic equation and in how many seconds with Jake hit the water?

User NeARAZ
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1 Answer

1 vote

Answer:

The time it will take Jake to hit the water ia approximately 4.46 seconds

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.

User Sboisse
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