The jump from a high ledge into a pool, swimming across a pool, and climbing a ladder are all described by quadratic and linear functions.

Answer 1

The jump from a high ledge into a pool can be described by a quadratic function, as the height of the jump can be represented by the equation h(t) = -16t^2 + vt + h, where t is the time in seconds, v is the initial vertical velocity, and h is the initial height. The highest point of the jump occurs when the derivative of this function is zero, giving us the vertex of the parabola.

Swimming across a pool can be described by a linear function, as the distance traveled can be represented by the equation d(t) = vt, where d is the distance, t is the time in seconds, and v is the constant velocity at which the swimmer is moving. The slope of this function represents the swimmer's speed.

Climbing a ladder can also be described by a linear function, as the height climbed can be represented by the equation h(t) = vt, where h is the height climbed, t is the time in seconds, and v is the constant climbing speed. The slope of this function represents the climbing speed of the person on the ladder.