Class 11 Exam > Class 11 Questions > Choose the correct alternative (s)a)If the gr...
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Choose the correct alternative (s)
- a)If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h.
- b)The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n)
- c)The time of flight T and the horizontal range R of a projectile are connected by the equation gT2 = 2Rtanq where q is the angle of projection.
- d)A ball is thrown vertically up. Another ball is thrown at an angle q with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two ball 1 : 1.
Correct answer is option 'A,B,C,D'. Can you explain this answer?
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Verified Answer
Choose the correct alternative (s)a)If the greatest height to which a ...
Let A be the angle of projection and u be the velocity of projection.
(A) Maximum height = u²/2g
Range = (u²sin 2A)/g
Maximum range (at A = π/4) = u²/g
So, max range = 2 × max height
(A) Maximum height = u²/2g
Range = (u²sin 2A)/g
Maximum range (at A = π/4) = u²/g
So, max range = 2 × max height
(B) Max Height = u²sin²A/2g
Range = (2u²sin A cos A)/g
Range = n × Max Height
(2u²sin A cos A)/g = n × (u²sin²A)/2g
4sin A cos A = n × sin²A
tan A = 4/n
Range = (2u²sin A cos A)/g
Range = n × Max Height
(2u²sin A cos A)/g = n × (u²sin²A)/2g
4sin A cos A = n × sin²A
tan A = 4/n
(C) The displacement in y-direction is zero.
0 = (u sin A)t - gt²/2
t = 2u sin A/g
R = (2u²sin A cos A)/g
2u²sin A cos A = gR
Multiply by 2 tan A
4u²sin²A = 2gR tan A
(2u sin A)² = 2gR tan A
g²t²= 2gR tan A
gt²= 2R tan A
0 = (u sin A)t - gt²/2
t = 2u sin A/g
R = (2u²sin A cos A)/g
2u²sin A cos A = gR
Multiply by 2 tan A
4u²sin²A = 2gR tan A
(2u sin A)² = 2gR tan A
g²t²= 2gR tan A
gt²= 2R tan A
(D) For vertical motion, t = 2u/g
For projectile of, T = 2u sin A/g
If T = t it means sin A = 1 => A = π/2
So, both are vertical motions and hence thier maximum heights will be same (or) their ratio is 1:1
For projectile of, T = 2u sin A/g
If T = t it means sin A = 1 => A = π/2
So, both are vertical motions and hence thier maximum heights will be same (or) their ratio is 1:1
Most Upvoted Answer
Choose the correct alternative (s)a)If the greatest height to which a ...
Let A be the angle of projection and u be the velocity of projection.
(A) Maximum height = u²/2g
Range = (u²sin 2A)/g
Maximum range (at A = π/4) = u²/g
So, max range = 2 × max height
(B) Max Height = u²sin²A/2g
Range = (2u²sin A cos A)/g
Range = n × Max Height
(2u²sin A cos A)/g = n × (u²sin²A)/2g
4sin A cos A = n × sin²A
tan A = 4/n
(C) The displacement in y-direction is zero.
0 = (u sin A)t - gt²/2
t = 2u sin A/g
R = (2u²sin A cos A)/g
2u²sin A cos A = gR
multiply by 2 tan A
4u²sin²A = 2gR tan A
(2u sin A)² = 2gR tan A
g²t²= 2gR tan A
gt²= 2R tan A
(D) For vertical motion, t = 2u/g
For projectile of, T = 2u sin A/g
If T = t it means sin A = 1 => A = π/2
So, both are vertical motions and hence thier maximum heights will be same (or) their ratio is 1:1
Therefore all options are correct
(A) Maximum height = u²/2g
Range = (u²sin 2A)/g
Maximum range (at A = π/4) = u²/g
So, max range = 2 × max height
(B) Max Height = u²sin²A/2g
Range = (2u²sin A cos A)/g
Range = n × Max Height
(2u²sin A cos A)/g = n × (u²sin²A)/2g
4sin A cos A = n × sin²A
tan A = 4/n
(C) The displacement in y-direction is zero.
0 = (u sin A)t - gt²/2
t = 2u sin A/g
R = (2u²sin A cos A)/g
2u²sin A cos A = gR
multiply by 2 tan A
4u²sin²A = 2gR tan A
(2u sin A)² = 2gR tan A
g²t²= 2gR tan A
gt²= 2R tan A
(D) For vertical motion, t = 2u/g
For projectile of, T = 2u sin A/g
If T = t it means sin A = 1 => A = π/2
So, both are vertical motions and hence thier maximum heights will be same (or) their ratio is 1:1
Therefore all options are correct
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Community Answer
Choose the correct alternative (s)a)If the greatest height to which a ...
Projectile Motion
Projectile motion is the motion of an object that is projected into the air and then moves under the influence of gravity. Some important concepts related to projectile motion are:
- Range: The horizontal distance covered by the projectile before it hits the ground.
- Maximum height: The highest point reached by the projectile during its motion.
- Angle of projection: The angle at which the projectile is launched with respect to the horizontal.
- Time of flight: The time taken by the projectile to hit the ground after it is launched.
Now, let's look at each option given in the question and see which ones are correct.
a) If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance up to which he can throw the stone is 2h.
- This statement is true. The maximum height and maximum horizontal distance of a projectile are related to each other. The maximum horizontal distance is achieved when the projectile is launched at an angle of 45 degrees. In this case, the range is equal to the maximum height, which is h. Therefore, if the maximum height is h, the maximum horizontal distance is 2h.
b) The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n).
- This statement is also true. The range of a projectile is given by R = u^2 sin2θ/g, where u is the initial velocity of the projectile, θ is the angle of projection, and g is the acceleration due to gravity. The maximum height is given by H = u^2 sin^2θ/2g. If R = nH, then we can substitute these values and solve for θ to get tan_1(4/n).
c) The time of flight T and the horizontal range R of a projectile are connected by the equation gT^2 = 2Rtanθ where θ is the angle of projection.
- This statement is true. The time of flight of a projectile is given by T = 2usinθ/g, where u is the initial velocity of the projectile. The horizontal range is given by R = u^2 sin2θ/g. If we eliminate u from these equations, we can get the relation gT^2 = 2Rtanθ.
d) A ball is thrown vertically up. Another ball is thrown at an angle θ with the vertical. Both of them remain in the air for the same period of time. Then the ratio of heights attained by the two balls is 1:1.
- This statement is false. When a ball is thrown vertically up, its velocity becomes zero at the highest point, and then it falls back down. Therefore, the time of flight is twice the time taken to reach the maximum height. On the other hand, when a ball is thrown at an angle, it follows a curved trajectory, and the time of flight depends on the angle of projection. Therefore, the heights attained by the two balls will not be the same.
In conclusion, options a, b, and c are correct, while option d is false.
Projectile motion is the motion of an object that is projected into the air and then moves under the influence of gravity. Some important concepts related to projectile motion are:
- Range: The horizontal distance covered by the projectile before it hits the ground.
- Maximum height: The highest point reached by the projectile during its motion.
- Angle of projection: The angle at which the projectile is launched with respect to the horizontal.
- Time of flight: The time taken by the projectile to hit the ground after it is launched.
Now, let's look at each option given in the question and see which ones are correct.
a) If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance up to which he can throw the stone is 2h.
- This statement is true. The maximum height and maximum horizontal distance of a projectile are related to each other. The maximum horizontal distance is achieved when the projectile is launched at an angle of 45 degrees. In this case, the range is equal to the maximum height, which is h. Therefore, if the maximum height is h, the maximum horizontal distance is 2h.
b) The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n).
- This statement is also true. The range of a projectile is given by R = u^2 sin2θ/g, where u is the initial velocity of the projectile, θ is the angle of projection, and g is the acceleration due to gravity. The maximum height is given by H = u^2 sin^2θ/2g. If R = nH, then we can substitute these values and solve for θ to get tan_1(4/n).
c) The time of flight T and the horizontal range R of a projectile are connected by the equation gT^2 = 2Rtanθ where θ is the angle of projection.
- This statement is true. The time of flight of a projectile is given by T = 2usinθ/g, where u is the initial velocity of the projectile. The horizontal range is given by R = u^2 sin2θ/g. If we eliminate u from these equations, we can get the relation gT^2 = 2Rtanθ.
d) A ball is thrown vertically up. Another ball is thrown at an angle θ with the vertical. Both of them remain in the air for the same period of time. Then the ratio of heights attained by the two balls is 1:1.
- This statement is false. When a ball is thrown vertically up, its velocity becomes zero at the highest point, and then it falls back down. Therefore, the time of flight is twice the time taken to reach the maximum height. On the other hand, when a ball is thrown at an angle, it follows a curved trajectory, and the time of flight depends on the angle of projection. Therefore, the heights attained by the two balls will not be the same.
In conclusion, options a, b, and c are correct, while option d is false.
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Choose the correct alternative (s)a)If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h.b)The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n)c)The time of flight T and the horizontal range R of a projectile are connected by the equation gT2= 2Rtanq where q is the angle of projection.d)A ball is thrown vertically up. Another ball is thrown at an angle q with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two ball 1 : 1.Correct answer is option 'A,B,C,D'. Can you explain this answer?
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Choose the correct alternative (s)a)If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h.b)The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n)c)The time of flight T and the horizontal range R of a projectile are connected by the equation gT2= 2Rtanq where q is the angle of projection.d)A ball is thrown vertically up. Another ball is thrown at an angle q with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two ball 1 : 1.Correct answer is option 'A,B,C,D'. Can you explain this answer? 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 Choose the correct alternative (s)a)If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h.b)The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n)c)The time of flight T and the horizontal range R of a projectile are connected by the equation gT2= 2Rtanq where q is the angle of projection.d)A ball is thrown vertically up. Another ball is thrown at an angle q with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two ball 1 : 1.Correct answer is option 'A,B,C,D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Choose the correct alternative (s)a)If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h.b)The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n)c)The time of flight T and the horizontal range R of a projectile are connected by the equation gT2= 2Rtanq where q is the angle of projection.d)A ball is thrown vertically up. Another ball is thrown at an angle q with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two ball 1 : 1.Correct answer is option 'A,B,C,D'. Can you explain this answer?.
Choose the correct alternative (s)a)If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h.b)The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n)c)The time of flight T and the horizontal range R of a projectile are connected by the equation gT2= 2Rtanq where q is the angle of projection.d)A ball is thrown vertically up. Another ball is thrown at an angle q with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two ball 1 : 1.Correct answer is option 'A,B,C,D'. Can you explain this answer? 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 Choose the correct alternative (s)a)If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h.b)The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n)c)The time of flight T and the horizontal range R of a projectile are connected by the equation gT2= 2Rtanq where q is the angle of projection.d)A ball is thrown vertically up. Another ball is thrown at an angle q with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two ball 1 : 1.Correct answer is option 'A,B,C,D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Choose the correct alternative (s)a)If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h.b)The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n)c)The time of flight T and the horizontal range R of a projectile are connected by the equation gT2= 2Rtanq where q is the angle of projection.d)A ball is thrown vertically up. Another ball is thrown at an angle q with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two ball 1 : 1.Correct answer is option 'A,B,C,D'. Can you explain this answer?.
Solutions for Choose the correct alternative (s)a)If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h.b)The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n)c)The time of flight T and the horizontal range R of a projectile are connected by the equation gT2= 2Rtanq where q is the angle of projection.d)A ball is thrown vertically up. Another ball is thrown at an angle q with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two ball 1 : 1.Correct answer is option 'A,B,C,D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
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Choose the correct alternative (s)a)If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h.b)The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n)c)The time of flight T and the horizontal range R of a projectile are connected by the equation gT2= 2Rtanq where q is the angle of projection.d)A ball is thrown vertically up. Another ball is thrown at an angle q with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two ball 1 : 1.Correct answer is option 'A,B,C,D'. Can you explain this answer?, a detailed solution for Choose the correct alternative (s)a)If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h.b)The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n)c)The time of flight T and the horizontal range R of a projectile are connected by the equation gT2= 2Rtanq where q is the angle of projection.d)A ball is thrown vertically up. Another ball is thrown at an angle q with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two ball 1 : 1.Correct answer is option 'A,B,C,D'. Can you explain this answer? has been provided alongside types of Choose the correct alternative (s)a)If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h.b)The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n)c)The time of flight T and the horizontal range R of a projectile are connected by the equation gT2= 2Rtanq where q is the angle of projection.d)A ball is thrown vertically up. Another ball is thrown at an angle q with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two ball 1 : 1.Correct answer is option 'A,B,C,D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Choose the correct alternative (s)a)If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h.b)The angle of projection for a projectile motion whose range R is n times the maximum height is tan_1(4/n)c)The time of flight T and the horizontal range R of a projectile are connected by the equation gT2= 2Rtanq where q is the angle of projection.d)A ball is thrown vertically up. Another ball is thrown at an angle q with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained by the two ball 1 : 1.Correct answer is option 'A,B,C,D'. Can you explain this answer? tests, examples and also practice Class 11 tests.
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