In Week 4 we learned about quadratic equations. In physics aquadratic equation can be used to model projectile motion.Projectile motion can describe the movement of a baseball after ithas been hit by a bat, or the movement of a cannonball after it hasbeen shot from a cannon. A penny falling from the Empire StateBuilding can even be modeled with this equation!
The projectile motion equation is s(t)=-16t^2+vt+h where s(t)represents the distance or height of an object at time t, vrepresents the initial speed of the object in ft/s, and h is theinitial height of the object, measured in feet.
If an object is starting at rest, then v=0 (such as for a pennybeing dropped from a building). If the object is starting from theground, h=0. The baseball or cannonball situations, each have aninitial velocity. For example, the initial velocity of the baseballis based on the speed at which the ball comes at you (the speed ofthe pitch).
Come up with a situation that you can model with this equation.Describe the situation, and tell us what v and h are. Fill in thevalues so that you have a quadratic equation. If you do research tofind initial velocities, include the links to the websites whereyou found that information. If you would like to make up your ownnumbers as well, you can (be creative)!
Once you have your equation, find the maximum height as well asthe time it takes to reach that maximum. Then use your equation tofind when the object hits the ground (i.e. the x-intercepts).
Finally, use those three points as well as the initial height tosketch a graph. You can take a photo of it and include the image,or use an online graphing calculator and take a screenshot if thatis easier.
