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A body thrown vertically upwards with an initial velocity u reaches maximum height in 6 seconds. The ratio of the distances travelled by the body in the first second and the seventh second is (1) 1:1 (2) 11:1 (3) 1:2 (4) 1:11.
Please help me with the solution.as quick as possible.?
Please help me with the solution.as quick as possible.?
Most Upvoted Answer
A body thrown vertically upwards with an initial velocity u reaches ma...
Solution:
Let's assume the initial velocity u of the body is u m/s.
When the body is thrown vertically upwards, the acceleration due to gravity acts in the opposite direction to the motion of the body. Hence, the body will experience retardation and its velocity will decrease by g m/s^2 (where g is the acceleration due to gravity) every second until it reaches its maximum height.
Given, the body reaches its maximum height in 6 seconds. Therefore, using the first equation of motion, we can find the maximum height (h) attained by the body as follows:
v = u - gt
At maximum height, v = 0 (since the body momentarily comes to rest before falling back down)
Therefore, 0 = u - g(6)
=> 6g = u
=> h = ut - 1/2 gt^2
=> h = (6g)(6) - 1/2 g(6)^2
=> h = 108g
Now, we need to find the ratio of the distances travelled by the body in the first second and the seventh second.
Distance travelled in the first second:
Using the third equation of motion, we can find the distance travelled by the body in the first second as follows:
s = ut + 1/2 at^2
=> s = u(1) + 1/2 g(1)^2
=> s = u/2
Distance travelled in the seventh second:
Using the third equation of motion, we can find the distance travelled by the body in the seventh second as follows:
s = ut + 1/2 at^2
=> s = u(7) + 1/2 g(7)^2
=> s = 7u - 171/2 g
Therefore, the ratio of the distances travelled by the body in the first second and the seventh second is:
s1/s7 = (u/2)/(7u - 171/2 g)
=> s1/s7 = 1/(14 - 171/2)
=> s1/s7 = 1/11
Hence, the ratio of the distances travelled by the body in the first second and the seventh second is 1:11.
Therefore, option (4) is the correct answer.
Let's assume the initial velocity u of the body is u m/s.
When the body is thrown vertically upwards, the acceleration due to gravity acts in the opposite direction to the motion of the body. Hence, the body will experience retardation and its velocity will decrease by g m/s^2 (where g is the acceleration due to gravity) every second until it reaches its maximum height.
Given, the body reaches its maximum height in 6 seconds. Therefore, using the first equation of motion, we can find the maximum height (h) attained by the body as follows:
v = u - gt
At maximum height, v = 0 (since the body momentarily comes to rest before falling back down)
Therefore, 0 = u - g(6)
=> 6g = u
=> h = ut - 1/2 gt^2
=> h = (6g)(6) - 1/2 g(6)^2
=> h = 108g
Now, we need to find the ratio of the distances travelled by the body in the first second and the seventh second.
Distance travelled in the first second:
Using the third equation of motion, we can find the distance travelled by the body in the first second as follows:
s = ut + 1/2 at^2
=> s = u(1) + 1/2 g(1)^2
=> s = u/2
Distance travelled in the seventh second:
Using the third equation of motion, we can find the distance travelled by the body in the seventh second as follows:
s = ut + 1/2 at^2
=> s = u(7) + 1/2 g(7)^2
=> s = 7u - 171/2 g
Therefore, the ratio of the distances travelled by the body in the first second and the seventh second is:
s1/s7 = (u/2)/(7u - 171/2 g)
=> s1/s7 = 1/(14 - 171/2)
=> s1/s7 = 1/11
Hence, the ratio of the distances travelled by the body in the first second and the seventh second is 1:11.
Therefore, option (4) is the correct answer.
Community Answer
A body thrown vertically upwards with an initial velocity u reaches ma...
(2) 11 : 1
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A body thrown vertically upwards with an initial velocity u reaches maximum height in 6 seconds. The ratio of the distances travelled by the body in the first second and the seventh second is (1) 1:1 (2) 11:1 (3) 1:2 (4) 1:11. Please help me with the solution.as quick as possible.?
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A body thrown vertically upwards with an initial velocity u reaches maximum height in 6 seconds. The ratio of the distances travelled by the body in the first second and the seventh second is (1) 1:1 (2) 11:1 (3) 1:2 (4) 1:11. Please help me with the solution.as quick as possible.? 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 body thrown vertically upwards with an initial velocity u reaches maximum height in 6 seconds. The ratio of the distances travelled by the body in the first second and the seventh second is (1) 1:1 (2) 11:1 (3) 1:2 (4) 1:11. Please help me with the solution.as quick as possible.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body thrown vertically upwards with an initial velocity u reaches maximum height in 6 seconds. The ratio of the distances travelled by the body in the first second and the seventh second is (1) 1:1 (2) 11:1 (3) 1:2 (4) 1:11. Please help me with the solution.as quick as possible.?.
A body thrown vertically upwards with an initial velocity u reaches maximum height in 6 seconds. The ratio of the distances travelled by the body in the first second and the seventh second is (1) 1:1 (2) 11:1 (3) 1:2 (4) 1:11. Please help me with the solution.as quick as possible.? 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 body thrown vertically upwards with an initial velocity u reaches maximum height in 6 seconds. The ratio of the distances travelled by the body in the first second and the seventh second is (1) 1:1 (2) 11:1 (3) 1:2 (4) 1:11. Please help me with the solution.as quick as possible.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body thrown vertically upwards with an initial velocity u reaches maximum height in 6 seconds. The ratio of the distances travelled by the body in the first second and the seventh second is (1) 1:1 (2) 11:1 (3) 1:2 (4) 1:11. Please help me with the solution.as quick as possible.?.
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