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What is the Maximum Height in Projectile Motion?
Grade Level:
Class 10
AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine
Definition
What is it?
The Maximum Height in Projectile Motion is the highest point an object reaches when it is thrown or launched into the air. At this peak point, the object momentarily stops moving upwards before it starts falling down.
Simple Example
Quick Example
Imagine you are playing cricket and hit a six! The ball goes up, reaches its highest point in the sky, and then starts coming down towards the boundary. That highest point the cricket ball reaches is its Maximum Height.
Worked Example
Step-by-Step
Let's calculate the maximum height for a ball thrown upwards with an initial vertical speed of 20 m/s. We know that at maximum height, the final vertical speed (v) is 0 m/s. We use the formula: v^2 = u^2 + 2as, where 'u' is initial speed, 'a' is acceleration due to gravity (-9.8 m/s^2), and 's' is the displacement (maximum height, H).
1. Identify given values: u = 20 m/s, v = 0 m/s, a = -9.8 m/s^2.
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2. Write down the formula: v^2 = u^2 + 2as.
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3. Substitute the values: 0^2 = (20)^2 + 2 * (-9.8) * H.
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4. Simplify the equation: 0 = 400 - 19.6 * H.
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5. Rearrange to solve for H: 19.6 * H = 400.
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6. Calculate H: H = 400 / 19.6.
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7. H = 20.41 meters (approximately).
So, the Maximum Height reached is approximately 20.41 meters.
Why It Matters
Understanding maximum height is crucial for designing rockets and satellites in Space Technology, and for predicting ball trajectories in sports analytics. Engineers use this concept to build bridges and structures, and even doctors in Medicine use it to understand how fluids move in the body.
Common Mistakes
MISTAKE: Using the initial launch speed directly in calculations for vertical height. | CORRECTION: Remember to use only the vertical component of the initial velocity (u sin theta) when calculating maximum height, not the total initial speed.
MISTAKE: Forgetting that acceleration due to gravity (g) is negative when an object is moving upwards. | CORRECTION: Always use g = -9.8 m/s^2 (or -10 m/s^2 for simpler calculations) when the object is moving against gravity.
MISTAKE: Confusing maximum height with the total range of the projectile. | CORRECTION: Maximum height is the highest vertical distance achieved, while range is the total horizontal distance covered.
Practice Questions
Try It Yourself
QUESTION: A stone is thrown straight up with an initial vertical speed of 15 m/s. Assuming g = 10 m/s^2, what is the maximum height it reaches? | ANSWER: 11.25 meters
QUESTION: A football is kicked with an initial velocity of 25 m/s at an angle of 30 degrees to the horizontal. Calculate the maximum height it reaches. (Hint: Vertical component of velocity = u sin theta, g = 9.8 m/s^2) | ANSWER: Approximately 7.97 meters
QUESTION: If a projectile reaches a maximum height of 45 meters, what was its initial vertical velocity? Assume g = 9.8 m/s^2. | ANSWER: Approximately 29.69 m/s
MCQ
Quick Quiz
At the maximum height of a projectile's path, what is its vertical velocity?
Maximum and upwards
Zero
Maximum and downwards
Equal to its horizontal velocity
The Correct Answer Is:
B
At the highest point, the object momentarily stops moving upwards before starting to fall, so its vertical velocity becomes zero. Its horizontal velocity remains constant.
Real World Connection
In the Real World
Cricket analysts use maximum height calculations to understand how high a shot goes, helping them predict if it will be a six or caught. ISRO scientists use these same principles to calculate the trajectory and maximum altitude of rockets launched into space, ensuring they reach their target orbits.
Key Vocabulary
Key Terms
Projectile: An object thrown or launched into the air | Trajectory: The path followed by a projectile | Initial Velocity: The speed and direction at which an object begins its motion | Acceleration due to Gravity (g): The constant acceleration experienced by objects near Earth's surface, approximately 9.8 m/s^2 | Vertical Component: The part of the velocity that is directed upwards or downwards.
What's Next
What to Learn Next
Great job understanding Maximum Height! Next, you should explore 'Range of Projectile Motion'. This will teach you how far a projectile travels horizontally, building on what you've learned about its vertical journey.
