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Anyone can give me derivation of projectile motion , time of maximum height and maximum height of projectile?
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Derivation of Projectile Motion
- Projectile motion is the motion of an object that is projected into the air and then moves under the influence of gravity alone.
- The motion can be analyzed by breaking it into two components: horizontal and vertical.
- The horizontal component of the motion is constant and is given by:
- Distance = velocity x time (d = vt)
- The vertical component of the motion is affected by gravity and is given by:
- Vertical distance = (1/2) x acceleration due to gravity x time^2 (h = (1/2)gt^2)
- The velocity of the projectile at any point in time can be found by combining the horizontal and vertical components of the motion using vector addition.
Time of Maximum Height of Projectile
- The time of maximum height of a projectile can be found by using the formula for the vertical component of motion.
- At maximum height, the vertical distance traveled by the projectile is zero.
- Therefore, we can set the formula for the vertical distance equal to zero and solve for time:
- 0 = (1/2)gt^2
- t = 0 or t = sqrt(2h/g)
- The time of maximum height is therefore given by t = sqrt(2h/g).
Maximum Height of Projectile
- The maximum height of a projectile can be found by using the formula for the vertical component of motion.
- At maximum height, the vertical velocity of the projectile is zero.
- Therefore, we can use the formula for the vertical velocity of the projectile to solve for the maximum height:
- Vertical velocity = initial vertical velocity + acceleration due to gravity x time
- 0 = u + gt
- t = u/g
- Substituting t into the formula for the vertical distance:
- h = (1/2)g(u/g)^2
- The maximum height is therefore given by h = (u^2)/2g.
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Anyone can give me derivation of projectile motion , time of maximum height and maximum height of projectile?
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Anyone can give me derivation of projectile motion , time of maximum height and maximum height of projectile? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Anyone can give me derivation of projectile motion , time of maximum height and maximum height of projectile? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Anyone can give me derivation of projectile motion , time of maximum height and maximum height of projectile?.
Anyone can give me derivation of projectile motion , time of maximum height and maximum height of projectile? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Anyone can give me derivation of projectile motion , time of maximum height and maximum height of projectile? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Anyone can give me derivation of projectile motion , time of maximum height and maximum height of projectile?.
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