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A projectile is projected with 3 ICAP 4 j cap 5 I camp m per second projection is taken as origin and East north and vertically upward direction and taken as positive x y z directions respectively is equal to 10 metre per second -2 for in SI units location of particle when it is at its maximum height is?
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A projectile is projected with 3 ICAP 4 j cap 5 I camp m per secon...
Answer:
Given:
- Projectile is projected with 3i + 4j + 5k m/s
- Projection is taken as origin and East north and vertically upward direction and taken as positive x y z directions respectively
- Acceleration due to gravity is 10 m/s²
To Find:
- Location of particle when it is at its maximum height
Solution:
Step 1: Initial Velocity of Projectile
- The initial velocity of the projectile is given as 3i + 4j + 5k m/s
Step 2: Maximum Height Reached by Projectile
- The maximum height reached by the projectile can be calculated using the formula:
- H = u²sin²θ / 2g
- Where H = maximum height, u = initial velocity, θ = angle of projection, g = acceleration due to gravity
- As the angle of projection is not given, we can assume that the projectile is projected at an angle of 45°
- Therefore, θ = 45°
- Substituting the given values, we get:
- H = (3² + 4² +5²) / (2 * 10) = 5.5 m
Step 3: Time Taken to Reach Maximum Height
- The time taken by the projectile to reach the maximum height can be calculated using the formula:
- t = usinθ / g
- Substituting the given values, we get:
- t = (3i + 4j + 5k)sin45° / 10 = 0.56 s
Step 4: Location of Particle at Maximum Height
- At the maximum height, the velocity of the projectile becomes zero
- Therefore, the time taken to reach maximum height is equal to the time taken for the projectile to reach the maximum height and come back to the ground
- The location of the projectile at the maximum height can be calculated using the formula:
- s = ut + 1/2at²
- As the projectile is at its maximum height, the vertical component of the displacement is equal to the maximum height reached by the projectile, i.e., 5.5 m
- The horizontal component of the displacement is zero, as the projectile does not move horizontally at the maximum height
- Therefore, the location of the projectile at the maximum height is:
- s = 3i + 4j + 5.5k m
Final Answer:
- The location of the particle when it is at its maximum height is 3i + 4j + 5.5k m.
Given:
- Projectile is projected with 3i + 4j + 5k m/s
- Projection is taken as origin and East north and vertically upward direction and taken as positive x y z directions respectively
- Acceleration due to gravity is 10 m/s²
To Find:
- Location of particle when it is at its maximum height
Solution:
Step 1: Initial Velocity of Projectile
- The initial velocity of the projectile is given as 3i + 4j + 5k m/s
Step 2: Maximum Height Reached by Projectile
- The maximum height reached by the projectile can be calculated using the formula:
- H = u²sin²θ / 2g
- Where H = maximum height, u = initial velocity, θ = angle of projection, g = acceleration due to gravity
- As the angle of projection is not given, we can assume that the projectile is projected at an angle of 45°
- Therefore, θ = 45°
- Substituting the given values, we get:
- H = (3² + 4² +5²) / (2 * 10) = 5.5 m
Step 3: Time Taken to Reach Maximum Height
- The time taken by the projectile to reach the maximum height can be calculated using the formula:
- t = usinθ / g
- Substituting the given values, we get:
- t = (3i + 4j + 5k)sin45° / 10 = 0.56 s
Step 4: Location of Particle at Maximum Height
- At the maximum height, the velocity of the projectile becomes zero
- Therefore, the time taken to reach maximum height is equal to the time taken for the projectile to reach the maximum height and come back to the ground
- The location of the projectile at the maximum height can be calculated using the formula:
- s = ut + 1/2at²
- As the projectile is at its maximum height, the vertical component of the displacement is equal to the maximum height reached by the projectile, i.e., 5.5 m
- The horizontal component of the displacement is zero, as the projectile does not move horizontally at the maximum height
- Therefore, the location of the projectile at the maximum height is:
- s = 3i + 4j + 5.5k m
Final Answer:
- The location of the particle when it is at its maximum height is 3i + 4j + 5.5k m.
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A projectile is projected with 3 ICAP 4 j cap 5 I camp m per secon...
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A projectile is projected with 3 ICAP 4 j cap 5 I camp m per second projection is taken as origin and East north and vertically upward direction and taken as positive x y z directions respectively is equal to 10 metre per second -2 for in SI units location of particle when it is at its maximum height is?
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A projectile is projected with 3 ICAP 4 j cap 5 I camp m per second projection is taken as origin and East north and vertically upward direction and taken as positive x y z directions respectively is equal to 10 metre per second -2 for in SI units location of particle when it is at its maximum height is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A projectile is projected with 3 ICAP 4 j cap 5 I camp m per second projection is taken as origin and East north and vertically upward direction and taken as positive x y z directions respectively is equal to 10 metre per second -2 for in SI units location of particle when it is at its maximum height is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A projectile is projected with 3 ICAP 4 j cap 5 I camp m per second projection is taken as origin and East north and vertically upward direction and taken as positive x y z directions respectively is equal to 10 metre per second -2 for in SI units location of particle when it is at its maximum height is?.
A projectile is projected with 3 ICAP 4 j cap 5 I camp m per second projection is taken as origin and East north and vertically upward direction and taken as positive x y z directions respectively is equal to 10 metre per second -2 for in SI units location of particle when it is at its maximum height is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A projectile is projected with 3 ICAP 4 j cap 5 I camp m per second projection is taken as origin and East north and vertically upward direction and taken as positive x y z directions respectively is equal to 10 metre per second -2 for in SI units location of particle when it is at its maximum height is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A projectile is projected with 3 ICAP 4 j cap 5 I camp m per second projection is taken as origin and East north and vertically upward direction and taken as positive x y z directions respectively is equal to 10 metre per second -2 for in SI units location of particle when it is at its maximum height is?.
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