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What is projectile motion? Derive the expression for maximum height, time of flight and horizontal range of a projectile fired at an angle with horizontal?
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What is projectile motion? Derive the expression for maximum height, t...
Projectile Motion:
Projectile motion refers to the motion of an object that is thrown or projected into the air and is subject only to the force of gravity and air resistance (if any). The object follows a curved path known as a trajectory.
Expression for Maximum Height:
The maximum height (H) reached by a projectile can be calculated using the formula:
\[ H = \frac{v^2\sin^2\theta}{2g} \]
where:
- v is the initial velocity of the projectile,
- θ is the angle of projection,
- g is the acceleration due to gravity.
Expression for Time of Flight:
The time of flight (T) of a projectile is the total time it spends in the air and can be calculated using the formula:
\[ T = \frac{2v\sin\theta}{g} \]
Expression for Horizontal Range:
The horizontal range (R) of a projectile is the horizontal distance covered by the projectile before hitting the ground and can be calculated using the formula:
\[ R = \frac{v^2\sin2\theta}{g} \]
When a projectile is fired at an angle with the horizontal, it follows a curved path. The time of flight, maximum height, and horizontal range depend on the initial velocity and the angle of projection. By understanding these expressions, one can accurately predict the motion of a projectile in various scenarios.
Projectile motion refers to the motion of an object that is thrown or projected into the air and is subject only to the force of gravity and air resistance (if any). The object follows a curved path known as a trajectory.
Expression for Maximum Height:
The maximum height (H) reached by a projectile can be calculated using the formula:
\[ H = \frac{v^2\sin^2\theta}{2g} \]
where:
- v is the initial velocity of the projectile,
- θ is the angle of projection,
- g is the acceleration due to gravity.
Expression for Time of Flight:
The time of flight (T) of a projectile is the total time it spends in the air and can be calculated using the formula:
\[ T = \frac{2v\sin\theta}{g} \]
Expression for Horizontal Range:
The horizontal range (R) of a projectile is the horizontal distance covered by the projectile before hitting the ground and can be calculated using the formula:
\[ R = \frac{v^2\sin2\theta}{g} \]
When a projectile is fired at an angle with the horizontal, it follows a curved path. The time of flight, maximum height, and horizontal range depend on the initial velocity and the angle of projection. By understanding these expressions, one can accurately predict the motion of a projectile in various scenarios.
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What is projectile motion? Derive the expression for maximum height, time of flight and horizontal range of a projectile fired at an angle with horizontal?
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What is projectile motion? Derive the expression for maximum height, time of flight and horizontal range of a projectile fired at an angle with horizontal? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What is projectile motion? Derive the expression for maximum height, time of flight and horizontal range of a projectile fired at an angle with horizontal? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is projectile motion? Derive the expression for maximum height, time of flight and horizontal range of a projectile fired at an angle with horizontal?.
What is projectile motion? Derive the expression for maximum height, time of flight and horizontal range of a projectile fired at an angle with horizontal? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What is projectile motion? Derive the expression for maximum height, time of flight and horizontal range of a projectile fired at an angle with horizontal? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is projectile motion? Derive the expression for maximum height, time of flight and horizontal range of a projectile fired at an angle with horizontal?.
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