Direction Of Projectile At Given Height Above Point Of Projection Calculator

Formula Used:

\[ \theta_{pr} = \tan^{-1}\left( \frac{\sqrt{(v_{pm}^2 \cdot (\sin(\alpha_{pr}))^2 - 2 \cdot g \cdot h)}}{v_{pm} \cdot \cos(\alpha_{pr})} \right) \]

Direction of Motion of a Particle:

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1. What is Direction of Projectile at Given Height?

The direction of a projectile at a given height above the point of projection refers to the angle that the velocity vector makes with the horizontal at that specific point in the projectile's trajectory. This angle changes continuously throughout the motion.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \theta_{pr} = \tan^{-1}\left( \frac{\sqrt{(v_{pm}^2 \cdot (\sin(\alpha_{pr}))^2 - 2 \cdot g \cdot h)}}{v_{pm} \cdot \cos(\alpha_{pr})} \right) \]

Where:

\( \theta_{pr} \) — Direction of motion of the particle (degrees)
\( v_{pm} \) — Initial velocity of projectile motion (m/s)
\( \alpha_{pr} \) — Angle of projection (degrees)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( h \) — Height above point of projection (m)

Explanation: The formula calculates the angle of the velocity vector at a specific height by considering the vertical and horizontal components of velocity.

3. Importance of Projectile Direction Calculation

Details: Understanding the direction of a projectile at different heights is crucial for various applications including ballistics, sports physics, engineering applications, and understanding the fundamental principles of projectile motion.

4. Using the Calculator

Tips: Enter initial velocity in m/s, angle of projection in degrees (0-90), and height in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why does the direction change during projectile motion?
A: The direction changes because the vertical component of velocity decreases due to gravity while the horizontal component remains constant, causing the resultant velocity vector to change direction.

Q2: What is the direction at maximum height?
A: At maximum height, the vertical component of velocity becomes zero, so the direction is purely horizontal (0 degrees).

Q3: Can the direction be negative?
A: Yes, when the projectile is descending, the direction becomes negative relative to the horizontal, indicating it's moving downward.

Q4: What factors affect the direction at a given height?
A: The direction depends on initial velocity, projection angle, height above projection point, and gravitational acceleration.

Q5: Is this calculation valid for all heights?
A: The calculation is valid only for heights that the projectile actually reaches. If the input height exceeds the maximum height, the result may be mathematically undefined.