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A particle is projected from a horizontal floor with speed 10 m s−1 at an angle 30° with the floor, which strikes the floor after some time. Which of the following is correct?
- a)Velocity of particle will be perpendicular to initial direction two seconds after projection.
- b)Minimum speed of the particle will be 5√3 m s−1
- c)Displacement of the particle after half second will be 1/4√325 m.
- d)The particle will strike the floor at 2 sec.
Correct answer is option 'B,C'. Can you explain this answer?
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Most Upvoted Answer
A particle is projected from a horizontal floor with speed 10 m s−1 a...
Minimum speed of a projectile is at a point when it reaches its maximum height as there, vertical velocity becomes zero.
⇒ vmin = 10cos30o = 5√3 ms−1
Time of flight of the given projectile is
Maximum height attained is
Range of the projectile
Displacement of the projectile at half second
= 
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Community Answer
A particle is projected from a horizontal floor with speed 10 m s−1 a...
Velocity Components
When a particle is projected with a certain speed and angle, its velocity can be broken down into two components: one in the horizontal direction and one in the vertical direction. Let's analyze the given scenario in detail.
Initial Velocity Components:
- Horizontal component (Vx): Vx = V * cosθ (where V is the initial speed and θ is the angle with the floor)
- Vertical component (Vy): Vy = V * sinθ
Now, let's calculate the initial velocity components using the given values:
V = 10 m/s
θ = 30°
Vx = 10 * cos(30°) = 10 * (√3/2) = 5√3 m/s
Vy = 10 * sin(30°) = 10 * (1/2) = 5 m/s
Velocity Components with Time
As time progresses, the horizontal component of velocity remains constant because there is no acceleration in the horizontal direction. However, the vertical component of velocity changes due to the acceleration due to gravity.
Horizontal Component:
Vx remains constant at 5√3 m/s throughout the motion.
Vertical Component:
Vy changes with time due to the acceleration due to gravity (g = 9.8 m/s^2). The equation for vertical velocity with time is given by:
Vy = initial Vy - g * t
Now, let's calculate the vertical component of velocity at different time intervals:
At t = 0 s (initial):
Vy = 5 m/s
At t = 1 s:
Vy = 5 - 9.8 * 1 = -4.8 m/s
At t = 2 s:
Vy = 5 - 9.8 * 2 = -14.6 m/s
At t = 0.5 s:
Vy = 5 - 9.8 * 0.5 = 0.2 m/s
Displacement of the Particle
The displacement of the particle can be calculated using the equations of motion. As the particle is projected horizontally, its horizontal displacement remains constant throughout the motion. The vertical displacement can be calculated using the equation:
Vertical Displacement (Sy) = initial Vy * t + (1/2) * g * t^2
Let's calculate the vertical displacement at t = 0.5 s:
Sy = 0.2 * 0.5 + (1/2) * 9.8 * (0.5)^2
= 0.1 + (1/2) * 9.8 * 0.25
= 0.1 + 1.225
= 1.325 m
Therefore, the displacement of the particle after half a second is 1.325 m.
Conclusion
Based on the analysis, the correct options are:
b) The minimum speed of the particle will be 5√3 m/s (which is the initial horizontal component of velocity).
c) The displacement of the particle after half a second will be 1.325 m.
The other options are incorrect:
a) The velocity of the particle will not be perpendicular to the initial direction after two seconds. It will have a vertical component due to the acceleration due to gravity.
d) The particle will not strike the floor at 2 seconds as it strikes the floor before that.
When a particle is projected with a certain speed and angle, its velocity can be broken down into two components: one in the horizontal direction and one in the vertical direction. Let's analyze the given scenario in detail.
Initial Velocity Components:
- Horizontal component (Vx): Vx = V * cosθ (where V is the initial speed and θ is the angle with the floor)
- Vertical component (Vy): Vy = V * sinθ
Now, let's calculate the initial velocity components using the given values:
V = 10 m/s
θ = 30°
Vx = 10 * cos(30°) = 10 * (√3/2) = 5√3 m/s
Vy = 10 * sin(30°) = 10 * (1/2) = 5 m/s
Velocity Components with Time
As time progresses, the horizontal component of velocity remains constant because there is no acceleration in the horizontal direction. However, the vertical component of velocity changes due to the acceleration due to gravity.
Horizontal Component:
Vx remains constant at 5√3 m/s throughout the motion.
Vertical Component:
Vy changes with time due to the acceleration due to gravity (g = 9.8 m/s^2). The equation for vertical velocity with time is given by:
Vy = initial Vy - g * t
Now, let's calculate the vertical component of velocity at different time intervals:
At t = 0 s (initial):
Vy = 5 m/s
At t = 1 s:
Vy = 5 - 9.8 * 1 = -4.8 m/s
At t = 2 s:
Vy = 5 - 9.8 * 2 = -14.6 m/s
At t = 0.5 s:
Vy = 5 - 9.8 * 0.5 = 0.2 m/s
Displacement of the Particle
The displacement of the particle can be calculated using the equations of motion. As the particle is projected horizontally, its horizontal displacement remains constant throughout the motion. The vertical displacement can be calculated using the equation:
Vertical Displacement (Sy) = initial Vy * t + (1/2) * g * t^2
Let's calculate the vertical displacement at t = 0.5 s:
Sy = 0.2 * 0.5 + (1/2) * 9.8 * (0.5)^2
= 0.1 + (1/2) * 9.8 * 0.25
= 0.1 + 1.225
= 1.325 m
Therefore, the displacement of the particle after half a second is 1.325 m.
Conclusion
Based on the analysis, the correct options are:
b) The minimum speed of the particle will be 5√3 m/s (which is the initial horizontal component of velocity).
c) The displacement of the particle after half a second will be 1.325 m.
The other options are incorrect:
a) The velocity of the particle will not be perpendicular to the initial direction after two seconds. It will have a vertical component due to the acceleration due to gravity.
d) The particle will not strike the floor at 2 seconds as it strikes the floor before that.
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A particle is projected from a horizontal floor with speed 10 m s−1 at an angle 30° with the floor, which strikes the floor after some time. Which of the following is correct?a)Velocity of particle will be perpendicular to initial direction two seconds after projection.b)Minimum speed of the particle will be 5√3 m s−1c)Displacement of the particle after half second will be 1/4√325 m.d)The particle will strike the floor at 2 sec.Correct answer is option 'B,C'. Can you explain this answer?
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A particle is projected from a horizontal floor with speed 10 m s−1 at an angle 30° with the floor, which strikes the floor after some time. Which of the following is correct?a)Velocity of particle will be perpendicular to initial direction two seconds after projection.b)Minimum speed of the particle will be 5√3 m s−1c)Displacement of the particle after half second will be 1/4√325 m.d)The particle will strike the floor at 2 sec.Correct answer is option 'B,C'. Can you explain this answer? 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 projected from a horizontal floor with speed 10 m s−1 at an angle 30° with the floor, which strikes the floor after some time. Which of the following is correct?a)Velocity of particle will be perpendicular to initial direction two seconds after projection.b)Minimum speed of the particle will be 5√3 m s−1c)Displacement of the particle after half second will be 1/4√325 m.d)The particle will strike the floor at 2 sec.Correct answer is option 'B,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is projected from a horizontal floor with speed 10 m s−1 at an angle 30° with the floor, which strikes the floor after some time. Which of the following is correct?a)Velocity of particle will be perpendicular to initial direction two seconds after projection.b)Minimum speed of the particle will be 5√3 m s−1c)Displacement of the particle after half second will be 1/4√325 m.d)The particle will strike the floor at 2 sec.Correct answer is option 'B,C'. Can you explain this answer?.
A particle is projected from a horizontal floor with speed 10 m s−1 at an angle 30° with the floor, which strikes the floor after some time. Which of the following is correct?a)Velocity of particle will be perpendicular to initial direction two seconds after projection.b)Minimum speed of the particle will be 5√3 m s−1c)Displacement of the particle after half second will be 1/4√325 m.d)The particle will strike the floor at 2 sec.Correct answer is option 'B,C'. Can you explain this answer? 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 projected from a horizontal floor with speed 10 m s−1 at an angle 30° with the floor, which strikes the floor after some time. Which of the following is correct?a)Velocity of particle will be perpendicular to initial direction two seconds after projection.b)Minimum speed of the particle will be 5√3 m s−1c)Displacement of the particle after half second will be 1/4√325 m.d)The particle will strike the floor at 2 sec.Correct answer is option 'B,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is projected from a horizontal floor with speed 10 m s−1 at an angle 30° with the floor, which strikes the floor after some time. Which of the following is correct?a)Velocity of particle will be perpendicular to initial direction two seconds after projection.b)Minimum speed of the particle will be 5√3 m s−1c)Displacement of the particle after half second will be 1/4√325 m.d)The particle will strike the floor at 2 sec.Correct answer is option 'B,C'. Can you explain this answer?.
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A particle is projected from a horizontal floor with speed 10 m s−1 at an angle 30° with the floor, which strikes the floor after some time. Which of the following is correct?a)Velocity of particle will be perpendicular to initial direction two seconds after projection.b)Minimum speed of the particle will be 5√3 m s−1c)Displacement of the particle after half second will be 1/4√325 m.d)The particle will strike the floor at 2 sec.Correct answer is option 'B,C'. Can you explain this answer?, a detailed solution for A particle is projected from a horizontal floor with speed 10 m s−1 at an angle 30° with the floor, which strikes the floor after some time. Which of the following is correct?a)Velocity of particle will be perpendicular to initial direction two seconds after projection.b)Minimum speed of the particle will be 5√3 m s−1c)Displacement of the particle after half second will be 1/4√325 m.d)The particle will strike the floor at 2 sec.Correct answer is option 'B,C'. Can you explain this answer? has been provided alongside types of A particle is projected from a horizontal floor with speed 10 m s−1 at an angle 30° with the floor, which strikes the floor after some time. Which of the following is correct?a)Velocity of particle will be perpendicular to initial direction two seconds after projection.b)Minimum speed of the particle will be 5√3 m s−1c)Displacement of the particle after half second will be 1/4√325 m.d)The particle will strike the floor at 2 sec.Correct answer is option 'B,C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A particle is projected from a horizontal floor with speed 10 m s−1 at an angle 30° with the floor, which strikes the floor after some time. Which of the following is correct?a)Velocity of particle will be perpendicular to initial direction two seconds after projection.b)Minimum speed of the particle will be 5√3 m s−1c)Displacement of the particle after half second will be 1/4√325 m.d)The particle will strike the floor at 2 sec.Correct answer is option 'B,C'. Can you explain this answer? tests, examples and also practice JEE tests.
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