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A shell fired from the ground explodes into two fragments A and B somewhere before the highest point of its trajectory. The fragment A immediately comes to a instantaneous rest and then falls. Knowing that horizontal range of the shell would have been R, if it were not exploded, predict location of mass centre of two fragments relative to the location of firing, when fragment A hits the ground 1)in the air at the horizontal distance that is less than R.justify?
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A shell fired from the ground explodes into two fragments A and B some...
The motion of the shell can be analyzed as a projectile motion, where the shell is launched at an angle with the horizontal and follows a parabolic trajectory. The explosion of the shell into two fragments, A and B, occurs somewhere before the highest point of its trajectory.
To predict the location of the mass center of the two fragments relative to the location of firing when fragment A hits the ground, we need to consider the motion of both fragments separately.
1. Motion of Fragment A:
Fragment A immediately comes to an instantaneous rest after the explosion and then falls vertically downwards due to the force of gravity. The horizontal range of the shell, R, would have been the maximum horizontal distance traveled by the shell if it had not exploded. Since the explosion occurs before the highest point of the trajectory, the horizontal distance traveled by fragment A would be less than R.
2. Motion of Fragment B:
Fragment B continues its motion after the explosion, following the parabolic trajectory of the shell. It will reach its maximum height and then fall back to the ground. The horizontal range of fragment B would also be less than R since the explosion occurs before the highest point of the trajectory.
3. Location of Mass Center:
The mass center of the two fragments can be determined by considering the individual masses of fragment A and fragment B. The mass center is the weighted average of the positions of the two fragments, where the weights are the masses.
Since fragment A falls vertically downwards, its horizontal position can be considered as the point of explosion. Let's denote this position as (x_A, y_A).
Fragment B follows the parabolic trajectory of the shell, and its horizontal position can be denoted as (x_B, y_B).
To find the location of the mass center (x_m, y_m), we can use the formula:
x_m = (m_A * x_A + m_B * x_B) / (m_A + m_B)
y_m = (m_A * y_A + m_B * y_B) / (m_A + m_B)
where m_A and m_B are the masses of fragment A and fragment B, respectively.
In conclusion, when fragment A hits the ground at a horizontal distance less than R, the location of the mass center of the two fragments relative to the location of firing will depend on the specific values of x_A, y_A, x_B, y_B, m_A, and m_B. By using the above formulas, we can determine the exact position of the mass center.
To predict the location of the mass center of the two fragments relative to the location of firing when fragment A hits the ground, we need to consider the motion of both fragments separately.
1. Motion of Fragment A:
Fragment A immediately comes to an instantaneous rest after the explosion and then falls vertically downwards due to the force of gravity. The horizontal range of the shell, R, would have been the maximum horizontal distance traveled by the shell if it had not exploded. Since the explosion occurs before the highest point of the trajectory, the horizontal distance traveled by fragment A would be less than R.
2. Motion of Fragment B:
Fragment B continues its motion after the explosion, following the parabolic trajectory of the shell. It will reach its maximum height and then fall back to the ground. The horizontal range of fragment B would also be less than R since the explosion occurs before the highest point of the trajectory.
3. Location of Mass Center:
The mass center of the two fragments can be determined by considering the individual masses of fragment A and fragment B. The mass center is the weighted average of the positions of the two fragments, where the weights are the masses.
Since fragment A falls vertically downwards, its horizontal position can be considered as the point of explosion. Let's denote this position as (x_A, y_A).
Fragment B follows the parabolic trajectory of the shell, and its horizontal position can be denoted as (x_B, y_B).
To find the location of the mass center (x_m, y_m), we can use the formula:
x_m = (m_A * x_A + m_B * x_B) / (m_A + m_B)
y_m = (m_A * y_A + m_B * y_B) / (m_A + m_B)
where m_A and m_B are the masses of fragment A and fragment B, respectively.
In conclusion, when fragment A hits the ground at a horizontal distance less than R, the location of the mass center of the two fragments relative to the location of firing will depend on the specific values of x_A, y_A, x_B, y_B, m_A, and m_B. By using the above formulas, we can determine the exact position of the mass center.
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A shell fired from the ground explodes into two fragments A and B somewhere before the highest point of its trajectory. The fragment A immediately comes to a instantaneous rest and then falls. Knowing that horizontal range of the shell would have been R, if it were not exploded, predict location of mass centre of two fragments relative to the location of firing, when fragment A hits the ground 1)in the air at the horizontal distance that is less than R.justify?
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A shell fired from the ground explodes into two fragments A and B somewhere before the highest point of its trajectory. The fragment A immediately comes to a instantaneous rest and then falls. Knowing that horizontal range of the shell would have been R, if it were not exploded, predict location of mass centre of two fragments relative to the location of firing, when fragment A hits the ground 1)in the air at the horizontal distance that is less than R.justify? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A shell fired from the ground explodes into two fragments A and B somewhere before the highest point of its trajectory. The fragment A immediately comes to a instantaneous rest and then falls. Knowing that horizontal range of the shell would have been R, if it were not exploded, predict location of mass centre of two fragments relative to the location of firing, when fragment A hits the ground 1)in the air at the horizontal distance that is less than R.justify? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shell fired from the ground explodes into two fragments A and B somewhere before the highest point of its trajectory. The fragment A immediately comes to a instantaneous rest and then falls. Knowing that horizontal range of the shell would have been R, if it were not exploded, predict location of mass centre of two fragments relative to the location of firing, when fragment A hits the ground 1)in the air at the horizontal distance that is less than R.justify?.
A shell fired from the ground explodes into two fragments A and B somewhere before the highest point of its trajectory. The fragment A immediately comes to a instantaneous rest and then falls. Knowing that horizontal range of the shell would have been R, if it were not exploded, predict location of mass centre of two fragments relative to the location of firing, when fragment A hits the ground 1)in the air at the horizontal distance that is less than R.justify? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A shell fired from the ground explodes into two fragments A and B somewhere before the highest point of its trajectory. The fragment A immediately comes to a instantaneous rest and then falls. Knowing that horizontal range of the shell would have been R, if it were not exploded, predict location of mass centre of two fragments relative to the location of firing, when fragment A hits the ground 1)in the air at the horizontal distance that is less than R.justify? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shell fired from the ground explodes into two fragments A and B somewhere before the highest point of its trajectory. The fragment A immediately comes to a instantaneous rest and then falls. Knowing that horizontal range of the shell would have been R, if it were not exploded, predict location of mass centre of two fragments relative to the location of firing, when fragment A hits the ground 1)in the air at the horizontal distance that is less than R.justify?.
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