Final answer:
The function for the jumper's height over time, starting from 24 feet high with an initial velocity of 10 feet per second, under gravity's influence is y(t) = 24 + 10t - 16t² feet. This quadratic equation takes gravity's constant acceleration into account.
Step-by-step explanation:
To determine a function for a jumper who starts 24 feet high with an initial velocity of 10 feet per second, we must take gravity into account. In the context of Earth, gravity accelerates objects at a rate of 32 feet per second squared downward. Therefore, the function will be a quadratic equation because gravity's acceleration is a constant that affects the vertical component of the jumper's motion quadratically.
The standard form of the equation for the height ‘y’ in feet of an object under gravity over time ‘t’ in seconds when the initial height is ‘y0’ and the initial velocity is ‘v0’ is given by:
y(t) = y0 + v0t - (1/2)gt²
Using the given values, the jumper's height equation is:
y(t) = 24 + 10t - (1/2)(32)t²
This equation represents the path of the jumper over time taking into account the starting height, the initial velocity, and the gravitational pull.