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The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by y =(4t-2t^2) m and x=3t metre, where t is in second and point of projection is taken as origin. The angle of projection of projectile with vertical is -???? Pls explain it some one. correct and is 37 degree.?
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The position coordinates of a projectile projected from ground on a ce...
The position coordinates of the projectile are given by y = (4t - 2t^2) m and x = 3t m, where t is in seconds and the point of projection is taken as the origin.
To find the angle of projection with the vertical, we need to determine the slope of the projectile's trajectory at the point of projection. The slope of a curve is given by the derivative of the equation representing the curve.
Derivative of y with respect to x can be found by differentiating y with respect to t and dividing it by the differentiation of x with respect to t.
dy/dx = dy/dt / dx/dt
Differentiating y = (4t - 2t^2) with respect to t:
dy/dt = 4 - 4t
Differentiating x = 3t with respect to t:
dx/dt = 3
Substituting these values into the derivative equation:
dy/dx = (4 - 4t) / 3
To find the angle of projection with the vertical, we need to find the angle whose tangent is equal to the slope of the trajectory at the point of projection. Let's denote this angle as θ.
tan(θ) = (4 - 4t) / 3
Now, let's substitute t = 0 (point of projection) into the equation:
tan(θ) = (4 - 4(0)) / 3
tan(θ) = 4 / 3
Using a calculator, we can find the value of θ:
θ = tan^(-1)(4/3)
θ ≈ 53.13 degrees
Therefore, the angle of projection with the vertical is approximately 53.13 degrees.
To find the angle of projection with the vertical, we need to determine the slope of the projectile's trajectory at the point of projection. The slope of a curve is given by the derivative of the equation representing the curve.
Derivative of y with respect to x can be found by differentiating y with respect to t and dividing it by the differentiation of x with respect to t.
dy/dx = dy/dt / dx/dt
Differentiating y = (4t - 2t^2) with respect to t:
dy/dt = 4 - 4t
Differentiating x = 3t with respect to t:
dx/dt = 3
Substituting these values into the derivative equation:
dy/dx = (4 - 4t) / 3
To find the angle of projection with the vertical, we need to find the angle whose tangent is equal to the slope of the trajectory at the point of projection. Let's denote this angle as θ.
tan(θ) = (4 - 4t) / 3
Now, let's substitute t = 0 (point of projection) into the equation:
tan(θ) = (4 - 4(0)) / 3
tan(θ) = 4 / 3
Using a calculator, we can find the value of θ:
θ = tan^(-1)(4/3)
θ ≈ 53.13 degrees
Therefore, the angle of projection with the vertical is approximately 53.13 degrees.
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The position coordinates of a projectile projected from ground on a ce...
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The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by y =(4t-2t^2) m and x=3t metre, where t is in second and point of projection is taken as origin. The angle of projection of projectile with vertical is -???? Pls explain it some one. correct and is 37 degree.?
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The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by y =(4t-2t^2) m and x=3t metre, where t is in second and point of projection is taken as origin. The angle of projection of projectile with vertical is -???? Pls explain it some one. correct and is 37 degree.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by y =(4t-2t^2) m and x=3t metre, where t is in second and point of projection is taken as origin. The angle of projection of projectile with vertical is -???? Pls explain it some one. correct and is 37 degree.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by y =(4t-2t^2) m and x=3t metre, where t is in second and point of projection is taken as origin. The angle of projection of projectile with vertical is -???? Pls explain it some one. correct and is 37 degree.?.
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