Projectile motion...?

Projectile Motion

When any object is thrown from horizontal at an angle θ except 90°, then the path followed by it is called trajectory, the object is called projectile and its motion is called projectile motion.

If any object is thrown with velocity u, making an angle θ, from horizontal, then

• Horizontal component of initial velocity = u cos θ.
• Vertical component of initial velocity = u sin θ.
• Horizontal component of velocity (u cos θ) remains same during the whole journey as no acceleration is acting horizontally.
• Vertical component of velocity (u sin θ) decreases gradually and becomes zero at highest point of the path.
• At highest point, the velocity of the body is u cos θ in horizontal direction and the angle between the velocity and acceleration is 90°.

Important Points & Formulae of Projectile Motion

1. At highest point, the linear momentum is mu cos θ and the kinetic energy is (1/2)m(u cos θ)².
2. The horizontal displacement of the projectile after t seconds
   x = (u cos θ)t
3. The vertical displacement of the projectile after t seconds
   y = (u sin θ) t — (1/2)gt²
4. Equation of the path of projectile
   
5. The path of a projectile is parabolic.
6. Kinetic energy at lowest point = (1/2) mu²
7. Linear momentum at lowest point = mu
8. Acceleration of projectile is constant throughout the motion and it acts vertically downwards being equal to g.
9. Angular momentum of projectile = mu cos θ x h, where h denotes the height.
10. In case of angular projection, the angle between velocity and acceleration varies from 0° < θ < 180°.
11. The maximum height occurs when the projectile covers a horizontal distance equal to half of the horizontal range, i.e., R/2.
12. When the maximum range of projectile is R, then its maximum height is R/4.