Free Falling Objects

I wrote this post from my iPhone. Here is an Algebra 2 problem that many students will see when they reach Calculus. The problem involves using the Quadratic function to model the height or position of an object vs time as the object is shot or thrown in the air. The method in Calculus is much easier. For Algebra 2 students, this is the method used to solve the problem.

Problem: Find the maximum height of a ball shot up in the air from a platform of 10 feet if the initial velocity of the ball is 40 feet/second.

Solution: Let s(t) = position of the ball, t = time, g = gravity constant, v nought = initial velocity, s nought = initial height.

quadratic function:

s(t) = (1/2)gt^2 + (v nought)t + (s nought)

g = - 32 ft per second^2

v nought = 40 feet per second

s(t) = (1/2)(-32)t^2 + 40t + 10

s(t) = - 16t^2 + 40t + 10

The graph of the function is concave down. The axis of symmetry is a vertical line passing through the vertex with the equation, t = -b/(2a).

t = - (40)/((2)(-16)) = -40/-32 = 1.25 seconds

s (1.25) = 35 feet

The maximum height that the ball will travel is 35 feet.

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