Types of Projectile Motion

This page delves into various types of projectile motion, expanding on the concepts introduced in the previous page.

Downward Vertical Throw

A downward vertical throw is similar to free fall but with an initial downward velocity.

Key equations:

• Velocity: v = v₀ + gt
• Position: h = v₀t + ½gt²
• Velocity-position relationship: v² = v₀² + 2gh

Upward Vertical Throw

An upward vertical throw involves an object launched vertically upward against gravity.

Highlight: The time taken for an object to reach its maximum height is equal to the time it takes to fall back to its starting point.

The maximum height (h_max) reached is given by: h_max = v₀²/(2g)

Horizontal Projectile Motion

Horizontal projectile motion involves an object launched horizontally from a certain height.

Definition: Horizontal projectile motion combines constant horizontal velocity with accelerated vertical motion due to gravity.

Key equations:

• Horizontal position: x = v_x · t
• Vertical position: y = ½gt²
• Velocity: v = √(v_x² + v_y²)

Where v_x is the constant horizontal velocity and v_y is the changing vertical velocity.

Oblique Projectile Motion

This page focuses on oblique projectile motion, also known as eğik atış in Turkish.

Oblique projectile motion occurs when an object is launched at an angle to the horizontal.

Definition: Oblique projectile motion combines both horizontal and vertical components of velocity, resulting in a parabolic trajectory.

Key equations for oblique projectile motion:

• Initial horizontal velocity: v_x = v₀ · cos(θ)
• Initial vertical velocity: v_y = v₀ · sin(θ)
• Range (horizontal distance): X = (v₀² · sin(2θ)) / g
• Maximum height: h_max = (v₀² · sin²(θ)) / (2g)
• Time of flight: t = (2v₀ · sin(θ)) / g

Where v₀ is the initial velocity and θ is the launch angle.

Highlight: The maximum range for an oblique projectile is achieved at a launch angle of 45°.

The page includes an example problem involving a projectile launched horizontally at 30 m/s, demonstrating calculations for time of flight, range, and impact velocity.

Example: For a horizontally launched projectile at 30 m/s from a height of 80 m, the time of flight is 4 seconds, and the range is 120 m.

Additional Notes on Oblique Projectile Motion

• The trajectory is symmetrical, with the time to reach maximum height equal to the time to fall from maximum height.
• For two different angles that sum to 90°, the ranges will be equal if the initial velocities are the same.
• The velocity at any point can be calculated using the horizontal and vertical components: v = √(v_x² + v_y²)

Vocabulary: Menzil (range) is the horizontal distance traveled by a projectile from launch to landing.

The page concludes with a diagram illustrating the parabolic paths of projectiles launched at different angles, emphasizing the relationship between launch angle and range.