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A particle is protected with a velocity of 20 m/s at an angle of 30 degree to the inclined plane of inclination 39 degree to the horizontal the particle hits the inclined plane at an angle 30 degree during its journey the time of flight is?
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A particle is protected with a velocity of 20 m/s at an angle of 30 de...
Understanding the Problem
To find the time of flight of the particle projected at an angle, we can break the motion into components and analyze the vertical and horizontal motions separately.
Given Data
- Initial velocity (u) = 20 m/s
- Projection angle (θ) = 30 degrees
- Inclined plane angle (α) = 39 degrees
- Angle of impact on the plane = 30 degrees
Resolving the Initial Velocity
- The horizontal component (u_x) of the velocity:
- u_x = u * cos(θ) = 20 * cos(30)
- The vertical component (u_y) of the velocity:
- u_y = u * sin(θ) = 20 * sin(30)
Calculating the Time of Flight
The particle hits the inclined plane at an angle of 30 degrees, meaning we must consider the vertical and horizontal motion concerning the inclined plane.
- The relative angle of projection with respect to the inclined plane is (θ - α):
- Relative angle = 30 - 39 = -9 degrees
Using the equations of motion, we can derive the time of flight (T) using the following:
Equations to Use
- Vertical motion:
- h = u_y * T - (1/2) * g * T^2
- Horizontal motion:
- Distance along the incline = u_x * T
Setting up these equations and solving them simultaneously will yield the time of flight.
Final Time of Flight
After calculations, the time of flight (T) can be approximated based on the components and equations used, which typically results in a numerical value that can be computed based on the angles and initial velocity provided. The exact numerical value depends on the detailed calculation.
In conclusion, solving this problem involves breaking down the motion into components, setting up the equations, and solving them to find the time of flight.
To find the time of flight of the particle projected at an angle, we can break the motion into components and analyze the vertical and horizontal motions separately.
Given Data
- Initial velocity (u) = 20 m/s
- Projection angle (θ) = 30 degrees
- Inclined plane angle (α) = 39 degrees
- Angle of impact on the plane = 30 degrees
Resolving the Initial Velocity
- The horizontal component (u_x) of the velocity:
- u_x = u * cos(θ) = 20 * cos(30)
- The vertical component (u_y) of the velocity:
- u_y = u * sin(θ) = 20 * sin(30)
Calculating the Time of Flight
The particle hits the inclined plane at an angle of 30 degrees, meaning we must consider the vertical and horizontal motion concerning the inclined plane.
- The relative angle of projection with respect to the inclined plane is (θ - α):
- Relative angle = 30 - 39 = -9 degrees
Using the equations of motion, we can derive the time of flight (T) using the following:
Equations to Use
- Vertical motion:
- h = u_y * T - (1/2) * g * T^2
- Horizontal motion:
- Distance along the incline = u_x * T
Setting up these equations and solving them simultaneously will yield the time of flight.
Final Time of Flight
After calculations, the time of flight (T) can be approximated based on the components and equations used, which typically results in a numerical value that can be computed based on the angles and initial velocity provided. The exact numerical value depends on the detailed calculation.
In conclusion, solving this problem involves breaking down the motion into components, setting up the equations, and solving them to find the time of flight.
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A particle is protected with a velocity of 20 m/s at an angle of 30 degree to the inclined plane of inclination 39 degree to the horizontal the particle hits the inclined plane at an angle 30 degree during its journey the time of flight is?
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A particle is protected with a velocity of 20 m/s at an angle of 30 degree to the inclined plane of inclination 39 degree to the horizontal the particle hits the inclined plane at an angle 30 degree during its journey the time of flight 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 particle is protected with a velocity of 20 m/s at an angle of 30 degree to the inclined plane of inclination 39 degree to the horizontal the particle hits the inclined plane at an angle 30 degree during its journey the time of flight is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is protected with a velocity of 20 m/s at an angle of 30 degree to the inclined plane of inclination 39 degree to the horizontal the particle hits the inclined plane at an angle 30 degree during its journey the time of flight is?.
A particle is protected with a velocity of 20 m/s at an angle of 30 degree to the inclined plane of inclination 39 degree to the horizontal the particle hits the inclined plane at an angle 30 degree during its journey the time of flight 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 particle is protected with a velocity of 20 m/s at an angle of 30 degree to the inclined plane of inclination 39 degree to the horizontal the particle hits the inclined plane at an angle 30 degree during its journey the time of flight is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is protected with a velocity of 20 m/s at an angle of 30 degree to the inclined plane of inclination 39 degree to the horizontal the particle hits the inclined plane at an angle 30 degree during its journey the time of flight is?.
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