1. Projectile Motion Important points to consider:  The most straight-forward technique of solving these problems is to separate motion occurring in the ‘x’ direction and motion occurring in the ‘y’ direction.  Because we are considering no air friction, the body experiences an acceleration of zero in the ‘x’ direction. Therefore, v x is constant.  Because we are considering no air friction, movement in the ‘y’ direction is the same as a freely falling body:

2. Projectile Motion Important points to consider:  When finding travel time, remember that the projectile must travel up, stop, and travel back down. So, at the top of the path (maximum height) v y = 0.  It’s very important to realize that the travel time is equal for both the ‘y’ and ‘x’ directions.  Always draw a coordinate system and clearly mark values. This is an excellent use for subscripts.  In these free-fall problems, final velocity is not zero. v f is the velocity of the body just before reaching the end of the fall.

3. + y + x  v0v0 v 0 y v 0 x The Problem: A baseball is thrown with an initial velocity of 10 m/s at an angle 60 o above horizontal. Find the following values: 1.maximum height 2.travel time (time the ball is in the air) 3.distance traveled in the horizontal direction

4. In the “y” direction, treat the ball as though it was thrown vertically upward at 8.7 m/s. At the top According to our coordinate system

5. Find maximum height: 0 0

6. Find the time the ball is in the air. This is the time for the ball to rise 3.9 m and return to y = 0. Rise time: 0

7. Find fall time. Treat this as a freely-falling body, where: At the top

8. 0 0 So, yes, in the absence of air, it takes the same time to rise as it does to fall.

9. Finally, let’s find the distance the ball will travel in the horizontal (x) direction. Remember that The ball leaves with v ox = 5.0 m/s and continues at that constant velocity in the x-direction for 1.8 s. Acceleration in the x- direction is zero because there is no force to change the motion of the ball. Distance in x-dir.

10. 0 0