2. Deriving the Range Equation Or, how to get there from here

3. Keep in mind... Horizontal velocity REMAINS CONSTANT – No net force is acting horizontally so there is no horizontal acceleration Vertical velocity CHANGES – Acceleration due to gravity, ~9.81 m/s 2 – Caused by the unbalanced force of gravity acting on the object

4. y max x x R = 2x

5. y max x x R = 2x  vivi

6.  vivi v iy = v i sin  v x = v i cos 

7. y max x x R = 2x  vivi v iy = v i sin  v x =v i cos 

8. y max x x R = 2x  vivi

9. y max x x R = 2x  vivi At the top of the path, v fy = 0

10. y max x x R = 2x  vivi Substituting in

11. y max x x R = 2x  vivi Substituting in

12.  vivi v iy = v i sin  v x = v i cos  Remember that the initial velocity in the y-direction = v i sin 

13. y max x x R = 2x  vivi

14. The whole point here is to solve for x...

15. Remember that the range, R, = 2x