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A cannon fire shells at speed u, inclination of its barrel to the horizontal can be changed in steps del theta =1 ranging from theta =15 to theta =85 let Rn be range of projection at angle theta =n Del Rn = |Rn-Rn 1| For what value of n del Rn is maximum? Neglect air resistance?
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A cannon fire shells at speed u, inclination of its barrel to the hori...
Explanation:
- When a cannon fires a shell at speed u, it follows a parabolic path due to gravity.
- The range of projection is the horizontal distance traveled by the shell before it hits the ground.
- The range of projection can be calculated using the formula R = u^2*sin(2*theta)/g, where g is the acceleration due to gravity.
- The inclination of the cannon barrel to the horizontal can be changed in steps of del theta = 1, ranging from theta = 15 to theta = 85.
- Let Rn be the range of projection at angle theta = n.
- Del Rn = |Rn - Rn-1|, where Rn-1 is the range of projection at angle theta = n-1.
- To find the value of n for which del Rn is maximum, we need to find the value of n for which Rn is maximum.
- Since we are neglecting air resistance, the maximum range of projection occurs at an angle of 45 degrees.
- Therefore, Rn is maximum when n = 45.
- Del Rn is maximum when the difference between Rn and Rn-1 is maximum.
- Since Rn is maximum at n = 45, we need to find the value of n for which the difference between Rn and Rn-1 is maximum.
- Using the formula for Rn, we can calculate the difference between Rn and Rn-1 as follows:
Calculation:
- Del Rn = |Rn - Rn-1|
- Del Rn = |u^2*sin(2*n*pi/180)/g - u^2*sin(2*(n-1)*pi/180)/g|
- Del Rn = |u^2/g * (sin(2*n*pi/180) - sin(2*(n-1)*pi/180))|
- Del Rn = |2*u^2/g * cos((2*n-1)*pi/360) * sin(pi/360)|
- Del Rn = 2*u^2/g * cos((2*n-1)*pi/360)
Conclusion:
- Therefore, the value of n for which del Rn is maximum is the value of n for which cos((2*n-1)*pi/360) is maximum.
- Since cos((2*n-1)*pi/360) is maximum when (2*n-1)*pi/360 = 0, pi, 2*pi, ..., the value of n for which del Rn is maximum is n = 23 or n = 24.
- Therefore, the maximum value of del Rn is 2*u^2/g.
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A cannon fire shells at speed u, inclination of its barrel to the horizontal can be changed in steps del theta =1 ranging from theta =15 to theta =85 let Rn be range of projection at angle theta =n Del Rn = |Rn-Rn 1| For what value of n del Rn is maximum? Neglect air resistance?
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A cannon fire shells at speed u, inclination of its barrel to the horizontal can be changed in steps del theta =1 ranging from theta =15 to theta =85 let Rn be range of projection at angle theta =n Del Rn = |Rn-Rn 1| For what value of n del Rn is maximum? Neglect air resistance? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A cannon fire shells at speed u, inclination of its barrel to the horizontal can be changed in steps del theta =1 ranging from theta =15 to theta =85 let Rn be range of projection at angle theta =n Del Rn = |Rn-Rn 1| For what value of n del Rn is maximum? Neglect air resistance? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cannon fire shells at speed u, inclination of its barrel to the horizontal can be changed in steps del theta =1 ranging from theta =15 to theta =85 let Rn be range of projection at angle theta =n Del Rn = |Rn-Rn 1| For what value of n del Rn is maximum? Neglect air resistance?.
A cannon fire shells at speed u, inclination of its barrel to the horizontal can be changed in steps del theta =1 ranging from theta =15 to theta =85 let Rn be range of projection at angle theta =n Del Rn = |Rn-Rn 1| For what value of n del Rn is maximum? Neglect air resistance? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A cannon fire shells at speed u, inclination of its barrel to the horizontal can be changed in steps del theta =1 ranging from theta =15 to theta =85 let Rn be range of projection at angle theta =n Del Rn = |Rn-Rn 1| For what value of n del Rn is maximum? Neglect air resistance? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cannon fire shells at speed u, inclination of its barrel to the horizontal can be changed in steps del theta =1 ranging from theta =15 to theta =85 let Rn be range of projection at angle theta =n Del Rn = |Rn-Rn 1| For what value of n del Rn is maximum? Neglect air resistance?.
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