As of 2011 the mens outdoor high jump record was held by Jav

As of 2011, the men\'s outdoor high jump record was held by Javier Sotomayor of Cuba. On July 27, 1993, he jumped 2.45 meters (8 feet 1 2 inch) into the air.

A) Create a quadratic function to model the situation. (Hint: The height above the ground of a person t seconds after he jumps into the air can be modeled by s(t) = 16(t h)2 + k feet, where h is the time he reaches his maximum height and k is the maximum height (in feet).) (Round your values to four decimal places.)

s(t) =

B) Assuming air resistance was negligible and that he landed on a cushion 2 feet above the height from which he jumped, how long was he airborne? (Round your answer to two decimal places.) _____sec

Solution

Quadratic functions are those functions with a degree of 2. What this means is that they will have, at most, three terms, and the highest exponent is always a 2. Yes, quadratic functions will always have the term with the exponent of 2.

The general or standard form of all quadratic functions is f(x) = ax^2 + bx + c, where a, b, and c are your coefficients, and x is your variable. Your coefficients can be any number. If a coefficient is 0, then it makes that term disappear. For quadratic functions, though, because the ax^2 term always needs to be present, the coefficient of a cannot be 0.

Your variable, x, can be any letter that is convenient for the function. If we are talking about time, our variable can be t. If we are talking about height, then our variable can be h. Our variable can be any letter that makes our function easy to understand.

b)

The length of time he is airborne is equal to the time he takes to hit the mat. The time taken to hit the mat is the time at which he reaches a height of 2 feet.

So you need to solve the equation

2 = -16(t-0.7089)^2+8.0417

It\'s a quadratic equation. It would be helpful to rearrange into the form
ax^2 + bx + c = 0 and use the quadratic formula.

This will give two solutions. The smallest will be the time to reach a height of 2 ft on the way UP, the greatest is the time taken to reach a height of 2 ft on the way DOWN, so your answer will be the largest of the two solutions