1. What is the Maximum Height Formula?

The maximum height formula calculates the highest point reached by a projectile (like a golf ball) launched at an angle. It's derived from the equations of motion under constant gravitational acceleration.

2. How Does the Calculator Work?

The calculator uses the maximum height formula:

Where:

• \( h \) — Maximum height (meters)
• \( v \) — Initial velocity (m/s)
• \( \theta \) — Launch angle (degrees)
• \( g \) — Gravitational acceleration (m/s², typically 9.81)

Explanation: The formula calculates the peak height of a projectile's trajectory, which occurs when the vertical velocity component becomes zero.

3. Importance of Maximum Height Calculation

Details: Calculating maximum height is crucial in sports physics, ballistics, and engineering applications to understand projectile behavior and optimize performance.

4. Using the Calculator

Tips: Enter initial velocity in m/s, launch angle in degrees (0-90), and gravitational acceleration (default is 9.81 m/s² for Earth). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is the sine function squared in the formula?
A: The sine function is squared because both the vertical velocity component and the time to reach maximum height depend on sin(θ).

Q2: 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.

Q3: Does air resistance affect the calculation?
A: Yes, this formula assumes no air resistance. In reality, air resistance reduces the actual maximum height.

Q4: Can this formula be used for any projectile?
A: Yes, it applies to any projectile motion under constant gravity, assuming no air resistance and flat surface.

Q5: How does gravity affect the maximum height?
A: Higher gravitational acceleration results in lower maximum height, as gravity pulls the object downward more strongly.