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Maximum Height Formula:
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The maximum height of a ball thrown upward is the highest vertical position it reaches before starting to fall back down. This occurs when the ball's vertical velocity becomes zero due to gravity's deceleration.
The calculator uses the maximum height formula:
Where:
Explanation: This formula is derived from the equations of motion under constant acceleration. At maximum height, the final velocity becomes zero, and we can solve for the displacement.
Details: Calculating maximum height is essential in physics, engineering, and sports science. It helps understand projectile motion, optimize athletic performance, and design various mechanical systems.
Tips: Enter the initial velocity in meters per second. The gravity value defaults to Earth's gravity (9.81 m/s²) but can be adjusted for other celestial bodies. All values must be positive numbers.
Q1: Does air resistance affect the maximum height?
A: Yes, in real-world scenarios, air resistance reduces the maximum height achieved compared to the theoretical calculation which assumes vacuum conditions.
Q2: How does throwing angle affect maximum height?
A: This calculator assumes vertical throwing (90° angle). For other angles, only the vertical component of velocity contributes to maximum height.
Q3: What's the relationship between initial velocity and maximum height?
A: Maximum height is proportional to the square of the initial velocity. Doubling the velocity quadruples the maximum height.
Q4: Can this formula be used on other planets?
A: Yes, simply adjust the gravity value to match the gravitational acceleration of the celestial body in question.
Q5: How is time to reach maximum height calculated?
A: Time to reach maximum height can be calculated using t = v/g, where v is initial velocity and g is gravitational acceleration.