Maximum Height Of Projectile On Horizontal Plane Calculator

Maximum Height Formula:

\[ h_{max} = \frac{v_{pm}^2 \cdot \sin(\alpha_{pr})^2}{2 \cdot [g]} \]

Maximum Height:

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1. What is Maximum Height of Projectile?

The maximum height of a projectile is the highest vertical position reached during its motion. It occurs when the vertical component of velocity becomes zero. This calculation is fundamental in projectile motion physics.

2. How Does the Calculator Work?

The calculator uses the maximum height formula:

\[ h_{max} = \frac{v_{pm}^2 \cdot \sin(\alpha_{pr})^2}{2 \cdot [g]} \]

Where:

\( h_{max} \) — Maximum height (meters)
\( v_{pm} \) — Initial velocity of projectile motion (m/s)
\( \alpha_{pr} \) — Angle of projection (radians)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)

Explanation: The formula calculates the peak height reached by a projectile launched at an angle, considering the initial velocity, launch angle, and gravitational acceleration.

3. Importance of Maximum Height Calculation

Details: Calculating maximum height is essential in various applications including sports analysis, engineering projectile trajectories, military applications, and understanding fundamental physics principles of motion.

4. Using the Calculator

Tips: Enter initial velocity in m/s and launch angle in degrees (0-90°). The calculator will automatically convert the angle to radians and compute the maximum height using the standard gravitational acceleration.

5. Frequently Asked Questions (FAQ)

Q1: What is the optimal angle for maximum height?
A: For maximum height alone, 90° (straight up) gives the highest possible height for a given initial velocity.

Q2: How does air resistance affect maximum height?
A: Air resistance reduces the maximum height achieved compared to the theoretical calculation in vacuum conditions.

Q3: Can this formula be used for any projectile?
A: This formula applies to ideal projectiles in uniform gravitational fields without air resistance.

Q4: What units should be used for inputs?
A: Velocity in meters per second (m/s) and angle in degrees. The calculator handles the conversion to radians.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for ideal conditions without air resistance or other external forces.