Projectile Peak Height Calculator

Projectile Peak Height Formula:

\[ Height = \frac{v^2 \times \sin^2 \theta}{2g} \]

Peak Height:

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1. What is Projectile Peak Height?

Projectile peak height is the maximum vertical displacement reached by a projectile during its flight. It's an important parameter in physics that describes the highest point in the trajectory of an object launched with an initial velocity at a specific angle.

2. How Does the Calculator Work?

The calculator uses the projectile peak height formula:

\[ Height = \frac{v^2 \times \sin^2 \theta}{2g} \]

Where:

\( v \) — Initial velocity (m/s)
\( \theta \) — Launch angle (degrees)
\( g \) — Gravitational acceleration (9.81 m/s²)

Explanation: The formula calculates the maximum height reached by a projectile based on its initial velocity and launch angle, assuming no air resistance and constant gravitational acceleration.

3. Importance of Peak Height Calculation

Details: Calculating peak height is essential in various applications including sports analysis, engineering projects, ballistics, and physics education. It helps predict the trajectory and behavior of projectiles in different scenarios.

4. Using the Calculator

Tips: Enter initial velocity in m/s and launch angle in degrees (0-90°). All values must be valid (velocity > 0, angle between 0-90).

5. Frequently Asked Questions (FAQ)

Q1: What is the optimal angle for maximum height?
A: For maximum height, the optimal launch angle is 90° (straight up), but this results in no horizontal distance traveled.

Q2: Does air resistance affect the calculation?
A: Yes, this formula assumes no air resistance. In real-world applications with significant air resistance, actual peak height will be lower than calculated.

Q3: How does gravity affect peak height?
A: Higher gravitational acceleration reduces peak height, while lower gravity (like on the moon) increases it for the same initial conditions.

Q4: What units should I use for the calculation?
A: Use consistent SI units: meters per second (m/s) for velocity, degrees for angle, and the result will be in meters (m).

Q5: Can this formula be used for any projectile?
A: This formula applies to any projectile motion where the only force acting is gravity (no air resistance, thrust, or other forces).