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A particle at a height h from the ground is projected with an angle 30 degree from the horizontal,it strikes the ground making angle 45 degree with horizontal.It is again projected from the same point at height h with the same speed but with angle of 60degree with horizontal.Find the angle it makes with the horizontal when it strikes the ground? Ans-tan inverse(√5)?
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A particle at a height h from the ground is projected with an angle 30...
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A particle at a height h from the ground is projected with an angle 30...
Given:
- Height of projection, h
- Angle of projection, θ1 = 30°
- Angle at which it strikes the ground, θ2 = 45°
- Angle of second projection, θ3 = 60°
To find:
Angle at which the particle strikes the ground, θ4
Assumptions:
- Neglect air resistance
- Take acceleration due to gravity, g = 9.8 m/s²
Analysis:
1. First Projection:
Let's analyze the first projection of the particle.
Initial velocity:
The initial velocity of the particle can be resolved into horizontal and vertical components.
- Horizontal component: u₁x = u₁ * cos(θ₁)
- Vertical component: u₁y = u₁ * sin(θ₁)
Time of flight:
The time taken by the particle to reach the ground can be calculated using the equation:
h = u₁y * t - (1/2) * g * t²
Using the quadratic formula, we can solve for t:
t = (u₁y ± √(u₁y² + 2gh)) / g
Since the particle is projected upwards, we take the positive root.
Range:
The horizontal distance covered by the particle can be calculated using the equation:
R = u₁x * t = u₁ * cos(θ₁) * t
2. Second Projection:
Let's analyze the second projection of the particle.
Initial velocity:
The initial velocity of the particle can be resolved into horizontal and vertical components.
- Horizontal component: u₂x = u₂ * cos(θ₃)
- Vertical component: u₂y = u₂ * sin(θ₃)
Time of flight:
Using the same equation as before, we can calculate the time of flight for the second projection.
Range:
Using the same equation as before, we can calculate the range for the second projection.
3. Finding θ4:
The angle at which the particle strikes the ground can be found by considering the horizontal and vertical components of its velocity at that instant.
Using the equation tan(θ₄) = (u₂y - u₁y) / (u₂x + u₁x), we can find θ₄.
Final Answer:
The angle at which the particle strikes the ground is tan inverse(√5).
- Height of projection, h
- Angle of projection, θ1 = 30°
- Angle at which it strikes the ground, θ2 = 45°
- Angle of second projection, θ3 = 60°
To find:
Angle at which the particle strikes the ground, θ4
Assumptions:
- Neglect air resistance
- Take acceleration due to gravity, g = 9.8 m/s²
Analysis:
1. First Projection:
Let's analyze the first projection of the particle.
Initial velocity:
The initial velocity of the particle can be resolved into horizontal and vertical components.
- Horizontal component: u₁x = u₁ * cos(θ₁)
- Vertical component: u₁y = u₁ * sin(θ₁)
Time of flight:
The time taken by the particle to reach the ground can be calculated using the equation:
h = u₁y * t - (1/2) * g * t²
Using the quadratic formula, we can solve for t:
t = (u₁y ± √(u₁y² + 2gh)) / g
Since the particle is projected upwards, we take the positive root.
Range:
The horizontal distance covered by the particle can be calculated using the equation:
R = u₁x * t = u₁ * cos(θ₁) * t
2. Second Projection:
Let's analyze the second projection of the particle.
Initial velocity:
The initial velocity of the particle can be resolved into horizontal and vertical components.
- Horizontal component: u₂x = u₂ * cos(θ₃)
- Vertical component: u₂y = u₂ * sin(θ₃)
Time of flight:
Using the same equation as before, we can calculate the time of flight for the second projection.
Range:
Using the same equation as before, we can calculate the range for the second projection.
3. Finding θ4:
The angle at which the particle strikes the ground can be found by considering the horizontal and vertical components of its velocity at that instant.
Using the equation tan(θ₄) = (u₂y - u₁y) / (u₂x + u₁x), we can find θ₄.
Final Answer:
The angle at which the particle strikes the ground is tan inverse(√5).
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A particle at a height h from the ground is projected with an angle 30 degree from the horizontal,it strikes the ground making angle 45 degree with horizontal.It is again projected from the same point at height h with the same speed but with angle of 60degree with horizontal.Find the angle it makes with the horizontal when it strikes the ground? Ans-tan inverse(√5)?
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A particle at a height h from the ground is projected with an angle 30 degree from the horizontal,it strikes the ground making angle 45 degree with horizontal.It is again projected from the same point at height h with the same speed but with angle of 60degree with horizontal.Find the angle it makes with the horizontal when it strikes the ground? Ans-tan inverse(√5)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A particle at a height h from the ground is projected with an angle 30 degree from the horizontal,it strikes the ground making angle 45 degree with horizontal.It is again projected from the same point at height h with the same speed but with angle of 60degree with horizontal.Find the angle it makes with the horizontal when it strikes the ground? Ans-tan inverse(√5)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle at a height h from the ground is projected with an angle 30 degree from the horizontal,it strikes the ground making angle 45 degree with horizontal.It is again projected from the same point at height h with the same speed but with angle of 60degree with horizontal.Find the angle it makes with the horizontal when it strikes the ground? Ans-tan inverse(√5)?.
A particle at a height h from the ground is projected with an angle 30 degree from the horizontal,it strikes the ground making angle 45 degree with horizontal.It is again projected from the same point at height h with the same speed but with angle of 60degree with horizontal.Find the angle it makes with the horizontal when it strikes the ground? Ans-tan inverse(√5)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A particle at a height h from the ground is projected with an angle 30 degree from the horizontal,it strikes the ground making angle 45 degree with horizontal.It is again projected from the same point at height h with the same speed but with angle of 60degree with horizontal.Find the angle it makes with the horizontal when it strikes the ground? Ans-tan inverse(√5)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle at a height h from the ground is projected with an angle 30 degree from the horizontal,it strikes the ground making angle 45 degree with horizontal.It is again projected from the same point at height h with the same speed but with angle of 60degree with horizontal.Find the angle it makes with the horizontal when it strikes the ground? Ans-tan inverse(√5)?.
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A particle at a height h from the ground is projected with an angle 30 degree from the horizontal,it strikes the ground making angle 45 degree with horizontal.It is again projected from the same point at height h with the same speed but with angle of 60degree with horizontal.Find the angle it makes with the horizontal when it strikes the ground? Ans-tan inverse(√5)?, a detailed solution for A particle at a height h from the ground is projected with an angle 30 degree from the horizontal,it strikes the ground making angle 45 degree with horizontal.It is again projected from the same point at height h with the same speed but with angle of 60degree with horizontal.Find the angle it makes with the horizontal when it strikes the ground? Ans-tan inverse(√5)? has been provided alongside types of A particle at a height h from the ground is projected with an angle 30 degree from the horizontal,it strikes the ground making angle 45 degree with horizontal.It is again projected from the same point at height h with the same speed but with angle of 60degree with horizontal.Find the angle it makes with the horizontal when it strikes the ground? Ans-tan inverse(√5)? theory, EduRev gives you an
ample number of questions to practice A particle at a height h from the ground is projected with an angle 30 degree from the horizontal,it strikes the ground making angle 45 degree with horizontal.It is again projected from the same point at height h with the same speed but with angle of 60degree with horizontal.Find the angle it makes with the horizontal when it strikes the ground? Ans-tan inverse(√5)? tests, examples and also practice JEE tests.
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