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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?
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Consider an ant crawling along the curve (x – 2)2 + y2 = 4, wher...
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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.
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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?
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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?.
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