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A gun can fire with a velocity u in all directions from a given position on a horizontal plane .the shots will fall on the plane within a circle of radius a) u/2g b) u/g c) u^2/2g d) u^2/g .(pl give an answer with explanation.)?
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A gun can fire with a velocity u in all directions from a given positi...
Solution:
The given problem can be solved using projectile motion equations.
- The equation of motion in the x-direction is given by: x = ut cosθ
- The equation of motion in the y-direction is given by: y = ut sinθ - 1/2gt^2
Since the gun can fire in all directions, we can assume that θ can take any value between 0° and 360°.
We need to find the radius of the circle within which all the shots will fall on the plane. This means that the maximum height reached by the projectile should be less than or equal to the height of the gun from the plane.
- The maximum height reached by the projectile is given by: H = u^2 sin^2θ/2g
- The height of the gun from the plane is given by: h = u^2/2g
Setting H = h, we get:
u^2 sin^2θ/2g = u^2/2g
sin^2θ = 1/2
sinθ = 1/√2 = cosθ
This means that the shots will fall on the plane at an angle of θ = 45° with the horizontal.
The range of the projectile is given by:
R = u^2 sin2θ/g
R = u^2 sin90°/g
R = u^2/g
Therefore, the radius of the circle within which all the shots will fall on the plane is:
R = u^2/g
Hence, the correct option is (d) u^2/g.
The given problem can be solved using projectile motion equations.
- The equation of motion in the x-direction is given by: x = ut cosθ
- The equation of motion in the y-direction is given by: y = ut sinθ - 1/2gt^2
Since the gun can fire in all directions, we can assume that θ can take any value between 0° and 360°.
We need to find the radius of the circle within which all the shots will fall on the plane. This means that the maximum height reached by the projectile should be less than or equal to the height of the gun from the plane.
- The maximum height reached by the projectile is given by: H = u^2 sin^2θ/2g
- The height of the gun from the plane is given by: h = u^2/2g
Setting H = h, we get:
u^2 sin^2θ/2g = u^2/2g
sin^2θ = 1/2
sinθ = 1/√2 = cosθ
This means that the shots will fall on the plane at an angle of θ = 45° with the horizontal.
The range of the projectile is given by:
R = u^2 sin2θ/g
R = u^2 sin90°/g
R = u^2/g
Therefore, the radius of the circle within which all the shots will fall on the plane is:
R = u^2/g
Hence, the correct option is (d) u^2/g.
Community Answer
A gun can fire with a velocity u in all directions from a given positi...
Oho it's simp
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A gun can fire with a velocity u in all directions from a given position on a horizontal plane .the shots will fall on the plane within a circle of radius a) u/2g b) u/g c) u^2/2g d) u^2/g .(pl give an answer with explanation.)?
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A gun can fire with a velocity u in all directions from a given position on a horizontal plane .the shots will fall on the plane within a circle of radius a) u/2g b) u/g c) u^2/2g d) u^2/g .(pl give an answer with explanation.)? 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 A gun can fire with a velocity u in all directions from a given position on a horizontal plane .the shots will fall on the plane within a circle of radius a) u/2g b) u/g c) u^2/2g d) u^2/g .(pl give an answer with explanation.)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A gun can fire with a velocity u in all directions from a given position on a horizontal plane .the shots will fall on the plane within a circle of radius a) u/2g b) u/g c) u^2/2g d) u^2/g .(pl give an answer with explanation.)?.
A gun can fire with a velocity u in all directions from a given position on a horizontal plane .the shots will fall on the plane within a circle of radius a) u/2g b) u/g c) u^2/2g d) u^2/g .(pl give an answer with explanation.)? 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 A gun can fire with a velocity u in all directions from a given position on a horizontal plane .the shots will fall on the plane within a circle of radius a) u/2g b) u/g c) u^2/2g d) u^2/g .(pl give an answer with explanation.)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A gun can fire with a velocity u in all directions from a given position on a horizontal plane .the shots will fall on the plane within a circle of radius a) u/2g b) u/g c) u^2/2g d) u^2/g .(pl give an answer with explanation.)?.
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A gun can fire with a velocity u in all directions from a given position on a horizontal plane .the shots will fall on the plane within a circle of radius a) u/2g b) u/g c) u^2/2g d) u^2/g .(pl give an answer with explanation.)?, a detailed solution for A gun can fire with a velocity u in all directions from a given position on a horizontal plane .the shots will fall on the plane within a circle of radius a) u/2g b) u/g c) u^2/2g d) u^2/g .(pl give an answer with explanation.)? has been provided alongside types of A gun can fire with a velocity u in all directions from a given position on a horizontal plane .the shots will fall on the plane within a circle of radius a) u/2g b) u/g c) u^2/2g d) u^2/g .(pl give an answer with explanation.)? theory, EduRev gives you an
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