Can u just explain how to do projectile motion and give examples of hroiontal velocityand displacement , verical velocity and displacement

Certainly! Projectile motion refers to the motion of an object that is launched into the air and moves under the influence of gravity, experiencing both horizontal and vertical motion simultaneously. To understand how to analyze projectile motion, we need to consider the following components:

1. Horizontal Velocity (Vx): This is the velocity of the object in the horizontal direction. In projectile motion, there is no acceleration acting horizontally, so the horizontal velocity remains constant throughout the motion. It can be calculated using the formula Vx = initial velocity * cos(angle), where the angle is the launch angle and the initial velocity is the speed at which the object is launched.

2. Horizontal Displacement (Dx): This is the distance covered by the object horizontally. It depends on the time of flight and the horizontal velocity. The formula to calculate horizontal displacement is Dx = Vx * time, where time is the total time of flight.

3. Vertical Velocity (Vy): This is the velocity of the object in the vertical direction and changes due to the effect of gravity. Initially, the object moves upward and then starts to fall downward. At the highest point, the vertical velocity becomes zero. It can be calculated using the formula Vy = initial velocity * sin(angle) - (gravity * time), where the gravity is the acceleration due to gravity (usually taken as 9.8 m/s²) and time is the total time of flight.

4. Vertical Displacement (Dy): This is the distance covered by the object vertically. It depends on the launch angle, initial velocity, and time of flight. The formula to calculate vertical displacement is Dy = (initial velocity * sin(angle) * time) - (0.5 * gravity * time²).

Now, let's consider an example:
Suppose an object is launched with an initial velocity of 20 m/s at an angle of 30 degrees with the horizontal. We can find the horizontal and vertical components of velocity and displacement.

1. Horizontal Velocity:
Vx = 20 m/s * cos(30°) = 20 m/s * √(3)/2 ≈ 17.32 m/s

2. Vertical Velocity:
Vy = 20 m/s * sin(30°) - (9.8 m/s² * t)

3. Horizontal Displacement:
Dx = Vx * t

4. Vertical Displacement:
Dy = (20 m/s * sin(30°) * t) - (0.5 * 9.8 m/s² * t²)

Please note that 't' represents the total time of flight.

By substituting the value of 't' into the equations, you can calculate the specific values for horizontal velocity, vertical velocity, horizontal displacement, and vertical displacement at different points during the projectile motion.