04-3d++Modeling+the+Flight+of+a+Ball

Any object that is tossed, or thrown, or launched into the air, such as a ball or even a rocket, is a projectile. We can use a quadratic function to model the height of the projectile at time t.



This model is for a projectile on Earth, and distances are measured in feet. The function would look different if we were on another planet with a different gravity, or if we were using the metric system. The function is also simplified, since it does not take into account wind, air resistance or any other real life situations. However, for our purposes, it is close enough.

Let's look at an example.

A football is kicked from ground level with an initial vertical velocity of 48 ft/sec. How long is the ball in the air?

Using the general equation for the path of a projectile, we can write:

The initial height is 0, since the football is at ground level. When the ball returns to ground level, its final height is also zero.

Now we set the equation equal to zero and solve for t:

At time t = 0 the ball is kicked, and it returns to the ground 3 second later, so it is in flight for 3 seconds.

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