GATE Exam > GATE Questions > Consider an ant crawling along the curve (x &...
Start Learning for Free
Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. The ant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters per second. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.
(Important - Enter only the numerical value in the answer)
Correct answer is '2'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Consider an ant crawling along the curve (x – 2)2 + y2 = 4, wher...
Most Upvoted Answer
Consider an ant crawling along the curve (x – 2)2 + y2 = 4, wher...
Let's say the ant starts at the point (x1, y1) and crawls along the curve (x, y) = (f(t), g(t)).
The velocity of the ant is given by the derivative of the position function with respect to time:
v(t) = (dx/dt, dy/dt) = (f'(t), g'(t))
The speed of the ant is the magnitude of the velocity vector:
|v(t)| = sqrt((f'(t))^2 + (g'(t))^2)
To find the point where the ant moves the fastest, we need to find the maximum value of |v(t)|. This occurs when the derivative of |v(t)| with respect to t is equal to zero:
d(|v(t)|)/dt = 0
Differentiating |v(t)| with respect to t:
d(|v(t)|)/dt = (f'(t) * f''(t) + g'(t) * g''(t)) / sqrt((f'(t))^2 + (g'(t))^2) = 0
This equation can be rearranged to:
(f'(t) * f''(t) + g'(t) * g''(t)) = 0
This equation represents the condition for the ant to move the fastest along the curve. By solving this equation, we can find the values of t where the ant moves the fastest.
The velocity of the ant is given by the derivative of the position function with respect to time:
v(t) = (dx/dt, dy/dt) = (f'(t), g'(t))
The speed of the ant is the magnitude of the velocity vector:
|v(t)| = sqrt((f'(t))^2 + (g'(t))^2)
To find the point where the ant moves the fastest, we need to find the maximum value of |v(t)|. This occurs when the derivative of |v(t)| with respect to t is equal to zero:
d(|v(t)|)/dt = 0
Differentiating |v(t)| with respect to t:
d(|v(t)|)/dt = (f'(t) * f''(t) + g'(t) * g''(t)) / sqrt((f'(t))^2 + (g'(t))^2) = 0
This equation can be rearranged to:
(f'(t) * f''(t) + g'(t) * g''(t)) = 0
This equation represents the condition for the ant to move the fastest along the curve. By solving this equation, we can find the values of t where the ant moves the fastest.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. Theant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters persecond. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer?
Question Description
Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. Theant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters persecond. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. Theant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters persecond. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. Theant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters persecond. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer?.
Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. Theant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters persecond. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. Theant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters persecond. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. Theant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters persecond. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer?.
Solutions for Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. Theant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters persecond. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. Theant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters persecond. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. Theant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters persecond. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer?, a detailed solution for Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. Theant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters persecond. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer? has been provided alongside types of Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. Theant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters persecond. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider an ant crawling along the curve (x – 2)2 + y2 = 4, where x and y are in meters. Theant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters persecond. The time taken by the ant to reach the point (2, 2) is (in seconds) _______.(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup