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kicyunya [14]
3 years ago
14

A trained stunt diver is diving off a platform that is 15 m high into a pool of water that is 45 cm deep. The height, h, in mete

rs, of the stunt diver above the water, is modeled by h=-4.9t^2+12t+5, where t is the time in seconds after starting the dive.
a) How long is the stunt diver above 15 m?

b) How long is the stunt diver in the air?
Mathematics
1 answer:
zepelin [54]3 years ago
8 0

Answer:

a) 0 seconds.

b) The stunt diver is in the air for 2.81 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}

x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}

\Delta = b^{2} - 4ac

Height of the diver after t seconds:

h(t) = -4.9t^2 + 12t + 5

a) How long is the stunt diver above 15 m?

Quadratic equation with a < 0, so the parabola is concave down, and it will be above 15m between the two roots that we found for h(t) = 15. So

h(t) = -4.9t^2 + 12t + 5

15 = -4.9t^2 + 12t + 5

-4.9t^2 + 12t - 10 = 0

Quadratic equation with a = -4.9, b = 12, c = -10. Then

\Delta = 12^{2} - 4(-4.9)(-10) = -52

Negative \Delta, which means that the stunt diver is never above 15m, so 0 seconds.

b) How long is the stunt diver in the air?

We have to find how long it takes for the diver to hit the ground, that is, t for which h(t) = 0. So

h(t) = -4.9t^2 + 12t + 5

0 = -4.9t^2 + 12t + 5

-4.9t^2 + 12t + 5 = 0

Quadratic equation with a = -4.9, b = 12, c = 5. Then

\Delta = 12^{2} - 4(-4.9)(5) = 242

x_{1} = \frac{-12 + \sqrt{242}}{2*(-4.9)} = -0.36

x_{2} = \frac{-12 - \sqrt{242}}{2*(4.9)} = 2.81

Time is a positive measure, so we take 2.81.

The stunt diver is in the air for 2.81 seconds.

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