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A stone is projected from level ground at t = 0 sec such that its horizontal and vertical components of initial velocity are 10 m/s and 20 m/s respectively. Then the instant of time (in seconds) at which tangential and normal components are acceleration of stone are same is : (neglected air resistance) g = 10m/s2
Correct answer is '3'. Can you explain this answer?
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Verified Answer
A stone is projected from level ground att= 0 sec such that its horizo...
Tangential acceleration
Normal acceleration 
During upward motion
During upward motion
⇒ vy = vz
uy – gt = ux
20 – 10t = 10
⇒ t = 1 sec
During downward motion
at = an
vy – vx
20 – 10t = – 10
⇒ t = 3 sec
uy – gt = ux
20 – 10t = 10
⇒ t = 1 sec
During downward motion
at = an
vy – vx
20 – 10t = – 10
⇒ t = 3 sec
The correct answer is: 3
Most Upvoted Answer
A stone is projected from level ground att= 0 sec such that its horizo...
Solution:
Given:
- Horizontal component of initial velocity, u_x = 10 m/s
- Vertical component of initial velocity, u_y = 20 m/s
To find:
The instant of time at which the tangential and normal components of acceleration are the same.
Analysis:
When a projectile is launched at an angle to the horizontal, its motion can be analyzed by breaking the initial velocity into horizontal and vertical components. The horizontal component remains constant throughout the motion, while the vertical component is affected by acceleration due to gravity.
Let's analyze the motion of the stone at a particular instant of time t.
- The horizontal component of velocity remains constant, so the horizontal component of acceleration is zero (a_x = 0).
- The vertical component of acceleration is due to gravity, directed downwards (a_y = -g).
At this instant, we can find the tangential and normal components of acceleration.
Tangential Component of Acceleration:
The tangential component of acceleration (a_t) is the component of acceleration along the direction of velocity.
- Since there is no horizontal acceleration (a_x = 0), the tangential component of acceleration is zero (a_t = 0).
Normal Component of Acceleration:
The normal component of acceleration (a_n) is the component of acceleration perpendicular to the direction of velocity.
- The vertical component of acceleration (a_y = -g) is also the normal component of acceleration (a_n) because it acts perpendicular to the velocity.
Since the tangential component of acceleration is zero (a_t = 0) and the normal component of acceleration is equal to the vertical component of acceleration (a_n = a_y = -g), we can conclude that the tangential and normal components of acceleration are the same.
Now, to find the time at which this occurs, we can use the equations of motion.
Vertical Motion of the Stone:
Using the equation of motion, we can find the time t when the stone reaches its highest point (when the vertical component of velocity becomes zero).
u_y = v_y + a_y * t
0 = u_y - g * t
Solving this equation for t, we get:
t = u_y / g
Substituting the values, we have:
t = 20 m/s / 10 m/s^2
t = 2 s
Since the stone takes 2 seconds to reach its highest point, it will take an equal amount of time to reach the instant when the tangential and normal components of acceleration are the same.
Therefore, the instant of time at which the tangential and normal components of acceleration are the same is 2 seconds.
Given:
- Horizontal component of initial velocity, u_x = 10 m/s
- Vertical component of initial velocity, u_y = 20 m/s
To find:
The instant of time at which the tangential and normal components of acceleration are the same.
Analysis:
When a projectile is launched at an angle to the horizontal, its motion can be analyzed by breaking the initial velocity into horizontal and vertical components. The horizontal component remains constant throughout the motion, while the vertical component is affected by acceleration due to gravity.
Let's analyze the motion of the stone at a particular instant of time t.
- The horizontal component of velocity remains constant, so the horizontal component of acceleration is zero (a_x = 0).
- The vertical component of acceleration is due to gravity, directed downwards (a_y = -g).
At this instant, we can find the tangential and normal components of acceleration.
Tangential Component of Acceleration:
The tangential component of acceleration (a_t) is the component of acceleration along the direction of velocity.
- Since there is no horizontal acceleration (a_x = 0), the tangential component of acceleration is zero (a_t = 0).
Normal Component of Acceleration:
The normal component of acceleration (a_n) is the component of acceleration perpendicular to the direction of velocity.
- The vertical component of acceleration (a_y = -g) is also the normal component of acceleration (a_n) because it acts perpendicular to the velocity.
Since the tangential component of acceleration is zero (a_t = 0) and the normal component of acceleration is equal to the vertical component of acceleration (a_n = a_y = -g), we can conclude that the tangential and normal components of acceleration are the same.
Now, to find the time at which this occurs, we can use the equations of motion.
Vertical Motion of the Stone:
Using the equation of motion, we can find the time t when the stone reaches its highest point (when the vertical component of velocity becomes zero).
u_y = v_y + a_y * t
0 = u_y - g * t
Solving this equation for t, we get:
t = u_y / g
Substituting the values, we have:
t = 20 m/s / 10 m/s^2
t = 2 s
Since the stone takes 2 seconds to reach its highest point, it will take an equal amount of time to reach the instant when the tangential and normal components of acceleration are the same.
Therefore, the instant of time at which the tangential and normal components of acceleration are the same is 2 seconds.
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A stone is projected from level ground att= 0 sec such that its horizontal and vertical components of initial velocity are 10m/sand 20m/srespectively. Then the instant of time (in seconds) at which tangential and normal components are acceleration of stone are same is : (neglected air resistance)g= 10m/s2Correct answer is '3'. Can you explain this answer?
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A stone is projected from level ground att= 0 sec such that its horizontal and vertical components of initial velocity are 10m/sand 20m/srespectively. Then the instant of time (in seconds) at which tangential and normal components are acceleration of stone are same is : (neglected air resistance)g= 10m/s2Correct answer is '3'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A stone is projected from level ground att= 0 sec such that its horizontal and vertical components of initial velocity are 10m/sand 20m/srespectively. Then the instant of time (in seconds) at which tangential and normal components are acceleration of stone are same is : (neglected air resistance)g= 10m/s2Correct answer is '3'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is projected from level ground att= 0 sec such that its horizontal and vertical components of initial velocity are 10m/sand 20m/srespectively. Then the instant of time (in seconds) at which tangential and normal components are acceleration of stone are same is : (neglected air resistance)g= 10m/s2Correct answer is '3'. Can you explain this answer?.
A stone is projected from level ground att= 0 sec such that its horizontal and vertical components of initial velocity are 10m/sand 20m/srespectively. Then the instant of time (in seconds) at which tangential and normal components are acceleration of stone are same is : (neglected air resistance)g= 10m/s2Correct answer is '3'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A stone is projected from level ground att= 0 sec such that its horizontal and vertical components of initial velocity are 10m/sand 20m/srespectively. Then the instant of time (in seconds) at which tangential and normal components are acceleration of stone are same is : (neglected air resistance)g= 10m/s2Correct answer is '3'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is projected from level ground att= 0 sec such that its horizontal and vertical components of initial velocity are 10m/sand 20m/srespectively. Then the instant of time (in seconds) at which tangential and normal components are acceleration of stone are same is : (neglected air resistance)g= 10m/s2Correct answer is '3'. Can you explain this answer?.
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