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One second after projection, a stone moves at an angle 45degree with the horizontal .two seconds after projection , it moves horizontally,its angle of projection is_
a. tan^-1(root(3))
b. tan^-1(4)
c. tan^-1(3)
d.tan^-1(2)?
a. tan^-1(root(3))
b. tan^-1(4)
c. tan^-1(3)
d.tan^-1(2)?
Most Upvoted Answer
One second after projection, a stone moves at an angle 45degree with t...
Solution:
Given:
- Angle of projection, θ = 45°
- Time after projection, t = 2 s
Concepts Used:
- Projectile motion
- Horizontal velocity, ux = u cos θ
- Vertical velocity, uy = u sin θ - gt
- Range, R = u2 sin 2θ / g
- Time of flight, T = 2u sin θ / g
Calculation:
Part 1: Finding the initial velocity, u
We know that the stone moves at an angle 45° with the horizontal one second after projection. Therefore, we can use the vertical velocity formula to find the initial velocity, u.
uy = u sin θ - gt
0 = u sin 45° - 9.8 × 1
u = 9.8 / sin 45°
u = 13.86 m/s
Part 2: Finding the angle of projection, α
We need to find the angle of projection when the stone moves horizontally, 2 seconds after projection. At this point, the vertical displacement of the stone is zero.
Using the vertical displacement formula, we can find the time taken by the stone to reach the highest point.
uy = u sin α - gt
0 = 13.86 sin α - 9.8t
t = 1.414 sec
The time taken to reach the highest point is half of the time of flight.
T = 2u sin θ / g
T = 2 × 13.86 sin 45° / 9.8
T = 2 sec
Therefore, the stone takes 1 second to reach the highest point.
At the highest point, the vertical velocity of the stone is zero. Using this, we can find the angle of projection.
uy = u sin α - gt
0 = 13.86 sin α - 9.8 × 2
sin α = 19.6 / 13.86
α = tan-1(19.6 / 13.86)
α = 57.99°
Answer:
The angle of projection when the stone moves horizontally, 2 seconds after projection, is 57.99° (option c).
Given:
- Angle of projection, θ = 45°
- Time after projection, t = 2 s
Concepts Used:
- Projectile motion
- Horizontal velocity, ux = u cos θ
- Vertical velocity, uy = u sin θ - gt
- Range, R = u2 sin 2θ / g
- Time of flight, T = 2u sin θ / g
Calculation:
Part 1: Finding the initial velocity, u
We know that the stone moves at an angle 45° with the horizontal one second after projection. Therefore, we can use the vertical velocity formula to find the initial velocity, u.
uy = u sin θ - gt
0 = u sin 45° - 9.8 × 1
u = 9.8 / sin 45°
u = 13.86 m/s
Part 2: Finding the angle of projection, α
We need to find the angle of projection when the stone moves horizontally, 2 seconds after projection. At this point, the vertical displacement of the stone is zero.
Using the vertical displacement formula, we can find the time taken by the stone to reach the highest point.
uy = u sin α - gt
0 = 13.86 sin α - 9.8t
t = 1.414 sec
The time taken to reach the highest point is half of the time of flight.
T = 2u sin θ / g
T = 2 × 13.86 sin 45° / 9.8
T = 2 sec
Therefore, the stone takes 1 second to reach the highest point.
At the highest point, the vertical velocity of the stone is zero. Using this, we can find the angle of projection.
uy = u sin α - gt
0 = 13.86 sin α - 9.8 × 2
sin α = 19.6 / 13.86
α = tan-1(19.6 / 13.86)
α = 57.99°
Answer:
The angle of projection when the stone moves horizontally, 2 seconds after projection, is 57.99° (option c).
Community Answer
One second after projection, a stone moves at an angle 45degree with t...
- At the topmost point of the projectile there is only horizontal velocity and no vertical velocity.
- After one second since it makes 45 degrees both its horizontal and vertical components of velocity are same
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One second after projection, a stone moves at an angle 45degree with the horizontal .two seconds after projection , it moves horizontally,its angle of projection is_a. tan^-1(root(3))b. tan^-1(4)c. tan^-1(3)d.tan^-1(2)?
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One second after projection, a stone moves at an angle 45degree with the horizontal .two seconds after projection , it moves horizontally,its angle of projection is_a. tan^-1(root(3))b. tan^-1(4)c. tan^-1(3)d.tan^-1(2)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about One second after projection, a stone moves at an angle 45degree with the horizontal .two seconds after projection , it moves horizontally,its angle of projection is_a. tan^-1(root(3))b. tan^-1(4)c. tan^-1(3)d.tan^-1(2)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One second after projection, a stone moves at an angle 45degree with the horizontal .two seconds after projection , it moves horizontally,its angle of projection is_a. tan^-1(root(3))b. tan^-1(4)c. tan^-1(3)d.tan^-1(2)?.
One second after projection, a stone moves at an angle 45degree with the horizontal .two seconds after projection , it moves horizontally,its angle of projection is_a. tan^-1(root(3))b. tan^-1(4)c. tan^-1(3)d.tan^-1(2)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about One second after projection, a stone moves at an angle 45degree with the horizontal .two seconds after projection , it moves horizontally,its angle of projection is_a. tan^-1(root(3))b. tan^-1(4)c. tan^-1(3)d.tan^-1(2)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One second after projection, a stone moves at an angle 45degree with the horizontal .two seconds after projection , it moves horizontally,its angle of projection is_a. tan^-1(root(3))b. tan^-1(4)c. tan^-1(3)d.tan^-1(2)?.
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