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Assignment:

Introduction:

The quadratic functions is often used to describe projectile motion. Objects thrown straight up or down in the air follow a parabolic motion.

For this situation, projectile path can be modeled by the function below which gives the height of an object h(t) at time t ,in seconds, for an object with initial velocity v0 and initial height h0 .

In meters: h(t)=4.9t2+v0t+h0

In feet: h(t)=16t2+v0t+h0

Scenario 1:

A potato is fired from a spud-gun at a height of 1.5 meters and with initial velocity of 25 meters per seconds. The equation modeled by this projectile motion is h(t)=4.9t2+25t+1.5

1. graph or sketch the projectile motion of the potato using a desmos calculator, attach a screenshot on your submission
2. what does the x-axis and y-axis means in the graph
3. what is the maximum height reached by this potato
4. what time does the potato reached the highest point
5. what time does the potato reached the ground, h(t)=0

Scenario 2:

A football is kicked from the ground, h0= 0, with an initial velocity of 35 feet per second.

1. Find the equation that modeled the height of a football, in feet at time t, in seconds
2. Sketch a graph using desmos graphing calculator, attach a screenshot of the graph
3. When will the football hits the ground at the end of its flight
4. Regulations for high school, NCAA and NFL require the goal post to be 10 feet above the ground. At what times is the ball 10 feet or higher above the ground?

Answer all questions and submit screenshots of all the graphs. You need to provide complete detailed solutions, showing work. Any questions answered from a graph must have the process explained.