Complete Handbook of Projectile
Motion
Advanced Analytical Treatment
Contents
1 Introduction to Projectile Motion 3
2 Kinematic Analysis 3
2.1 Resolution of Initial Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Position as a Function of Time . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 Velocity Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Equation of Trajectory 4
4 Important Physical Quantities 4
4.1 Time of Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4.2 Maximum Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4.3 Horizontal Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4.4 Height When Range is Maximum . . . . . . . . . . . . . . . . . . . . . . . . 5
5 Analytical Relations Between R, H and T 5
6 Velocity Direction Analysis 5
7 When Velocity is Perpendicular to Initial Velocity 6
8 Energy Considerations 6
9 Linear Momentum Changes 6
10 Angular Momentum About Projection Point 7
11 Projectile from Height 7
12 Horizontal Projection 7
1
, 13 Projectile on Inclined Plane 8
14 Area Covered for All Directions 8
15 Collision of Two Projectiles 8
16 Conceptual Observations 8
17 Extended Theoretical Discussion 9
18 Practice Problems 9
2
Motion
Advanced Analytical Treatment
Contents
1 Introduction to Projectile Motion 3
2 Kinematic Analysis 3
2.1 Resolution of Initial Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Position as a Function of Time . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 Velocity Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Equation of Trajectory 4
4 Important Physical Quantities 4
4.1 Time of Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4.2 Maximum Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4.3 Horizontal Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4.4 Height When Range is Maximum . . . . . . . . . . . . . . . . . . . . . . . . 5
5 Analytical Relations Between R, H and T 5
6 Velocity Direction Analysis 5
7 When Velocity is Perpendicular to Initial Velocity 6
8 Energy Considerations 6
9 Linear Momentum Changes 6
10 Angular Momentum About Projection Point 7
11 Projectile from Height 7
12 Horizontal Projection 7
1
, 13 Projectile on Inclined Plane 8
14 Area Covered for All Directions 8
15 Collision of Two Projectiles 8
16 Conceptual Observations 8
17 Extended Theoretical Discussion 9
18 Practice Problems 9
2
