Math Problem Statement

A ball thrown into the air from a building 100 ft high travels along a path described by y = -1+1+100, where y is the height in feet and z is the horizontal distance from the building in feet. What is the maximum height the ball will reach?

Solution

The equation you provided is:

y=1+1+100y = -1 + 1 + 100

This simplifies to:

y=100y = 100

It appears that the equation doesn’t model the ball's parabolic trajectory properly. A typical equation for a ball's path is quadratic, like:

y=ax2+bx+cy = -ax^2 + bx + c

where yy is the height, xx is the horizontal distance, and the constants aa, bb, and cc describe the motion.

If you meant to provide such a quadratic equation and simply made a typo, please clarify it. However, if the equation truly simplifies to just y=100y = 100, it means the ball remains at a constant height of 100 feet without rising or falling.

Let me know if you intended a different form of the equation!


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Math Problem Analysis

Mathematical Concepts

Quadratic Equations
Parabolic Motion

Formulas

Standard form of a quadratic equation: y = ax^2 + bx + c

Theorems

Vertex formula for a parabola

Suitable Grade Level

Grades 9-12