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Height Formula (Projectile Motion):
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The height calculation in physics (specifically in projectile motion) determines the maximum vertical displacement of an object based on its initial and final velocities and the acceleration due to gravity. This formula is derived from the equations of motion.
The calculator uses the height formula:
Where:
Explanation: This equation comes from the kinematic equations of motion, specifically derived from the equation \( v^2 = u^2 + 2as \) where 'a' is acceleration (negative gravity in this case) and 's' is displacement (height).
Details: Calculating maximum height is crucial in projectile motion problems, helping to analyze trajectories in sports, engineering applications, and physics education. It's fundamental for understanding energy conservation as well.
Tips: Enter velocities in meters per second (m/s). For Earth's gravity, use 9.8 m/s². The calculator works for both upward and downward motion (use appropriate signs for direction).
Q1: What if the object is thrown downward?
A: Use negative values for initial velocity (u) if throwing downward. The calculator will give correct results based on the input directions.
Q2: Does this work for all planets?
A: Yes, just change the gravity value (g) to match the celestial body (3.71 m/s² for Mars, 24.79 m/s² for Jupiter, etc.).
Q3: What's the difference between height and range?
A: Height is vertical displacement, while range is horizontal distance traveled. Different formulas are used for each.
Q4: Can I use this for non-projectile motion?
A: This specific formula is for vertical motion under constant acceleration (gravity). Other formulas apply for different scenarios.
Q5: What if I only know time and initial velocity?
A: You would need to use a different formula: \( h = ut + \frac{1}{2}gt^2 \). This calculator focuses on the velocity-based formula.