Since its unaffected by gravity, the horizontal speed will be the magnitude of the horizontal component. The vertical position of the projectile after t time is the sum of the distance traveled due to the initial velocity and the distance traveled due to gravity. The problem situation can be a little more complicated if the object is not launched from the ground. The vertical height at the time of launch must be added to the expression for y . The following problem illustrates this concept.
Students write the parametric equations to model the path of the arrow.
Then they find the amount of time that it willl take the arrow to travel 70 meters horizontally. This is when the arrow will hit the target. Using that value of time in the expression for y , they find the vertical position. With the TI-82 in parametric mode it is possible to graph these equations to see the path of the projectile. One of the problems used in this section follows.