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A projectile is fired at a speed of 100m/s at an angle of 37' above the horizontal .at the highest point ,the projectile breaks into two parts of mass ratio 1:3 , the smaller coming to rest .find the distance from the launching point to the point where the heavier piece lands.?
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A projectile is fired at a speed of 100m/s at an angle of 37' above th...
Given:
Calculating Initial Components:
Calculating Time to Reach Highest Point:
Calculating Maximum Height:
Calculating Velocities of Projectile Parts:
Calculating Distance Travelled by Larger Projectile:
Therefore, the distance from the launching point to the point where the heavier piece lands is 550.2 m.
- Initial velocity (u) = 100 m/s
- Angle of projection (θ) = 37°
- Mass ratio of projectile at highest point = 1:3
- Final velocity of smaller projectile (v1) = 0 m/s
Calculating Initial Components:
- Initial horizontal velocity (ux) = u cos θ = 100 cos 37° = 79.87 m/s
- Initial vertical velocity (uy) = u sin θ = 100 sin 37° = 60.6 m/s
Calculating Time to Reach Highest Point:
- At the highest point, the vertical velocity becomes 0.
- Using the formula: uy = u sin θ - gt, where g = 9.8 m/s² (acceleration due to gravity)
- t = uy/g = 60.6/9.8 = 6.18 s
Calculating Maximum Height:
- Using the formula: h = (uy²/2g)
- h = (60.6²)/(2x9.8) = 185.93 m
Calculating Velocities of Projectile Parts:
- Using conservation of momentum: mu = mv1 + mv2, where mv1 and mv2 are the final velocities of the smaller and larger projectiles, respectively.
- Let the mass of the smaller projectile be m and the mass of the larger projectile be 3m.
- At the highest point, the velocities of both projectiles are equal and opposite.
- So, 100m = mv1 + 3mv2 and v1 = 0.
- Therefore, v2 = 100m/3m = 33.33 m/s
Calculating Distance Travelled by Larger Projectile:
- Using the formula: Range = (u²sin2θ)/g
- Range = (100²sin2(37°))/9.8 = 733.6 m
- The distance travelled by the larger projectile is 3/4 of the total range.
- Hence, the distance travelled by the larger projectile = (3/4) x 733.6 = 550.2 m
Therefore, the distance from the launching point to the point where the heavier piece lands is 550.2 m.
Community Answer
A projectile is fired at a speed of 100m/s at an angle of 37' above th...
Use momentum conservation on highest point and u got velocity use projectile formulas to fund distance traveled
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A projectile is fired at a speed of 100m/s at an angle of 37' above the horizontal .at the highest point ,the projectile breaks into two parts of mass ratio 1:3 , the smaller coming to rest .find the distance from the launching point to the point where the heavier piece lands.?
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A projectile is fired at a speed of 100m/s at an angle of 37' above the horizontal .at the highest point ,the projectile breaks into two parts of mass ratio 1:3 , the smaller coming to rest .find the distance from the launching point to the point where the heavier piece lands.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A projectile is fired at a speed of 100m/s at an angle of 37' above the horizontal .at the highest point ,the projectile breaks into two parts of mass ratio 1:3 , the smaller coming to rest .find the distance from the launching point to the point where the heavier piece lands.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A projectile is fired at a speed of 100m/s at an angle of 37' above the horizontal .at the highest point ,the projectile breaks into two parts of mass ratio 1:3 , the smaller coming to rest .find the distance from the launching point to the point where the heavier piece lands.?.
A projectile is fired at a speed of 100m/s at an angle of 37' above the horizontal .at the highest point ,the projectile breaks into two parts of mass ratio 1:3 , the smaller coming to rest .find the distance from the launching point to the point where the heavier piece lands.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A projectile is fired at a speed of 100m/s at an angle of 37' above the horizontal .at the highest point ,the projectile breaks into two parts of mass ratio 1:3 , the smaller coming to rest .find the distance from the launching point to the point where the heavier piece lands.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A projectile is fired at a speed of 100m/s at an angle of 37' above the horizontal .at the highest point ,the projectile breaks into two parts of mass ratio 1:3 , the smaller coming to rest .find the distance from the launching point to the point where the heavier piece lands.?.
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