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The horizontal distance of a kite from the boy flying it is 30 m and 50 m of cord is out from the roll. If the wind moves the kite horizontally at the rate of 5 km/h directly away from the boy, how fast is the cord being released?
- a)3 km/h
- b)4 km /h
- c)5 km/h
- d)6 km/h
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The horizontal distance of a kite from the boy flying it is 30 m and ...
Given data:
- Horizontal distance of the kite from the boy (x) = 30 m
- Length of the cord (l) = 50 m
- Rate at which the kite is moving horizontally (v) = 5 km/h
To find:
The rate at which the cord is being released
Concept:
In this problem, we can use the Pythagorean theorem to relate the horizontal distance of the kite from the boy (x), the length of the cord (l), and the height of the kite (h).
Solution:
Let's assume the height of the kite is h. According to the Pythagorean theorem, we have:
x^2 + h^2 = l^2
Differentiating both sides with respect to time, we get:
2x(dx/dt) + 2h(dh/dt) = 2l(dl/dt)
Since the height of the kite remains constant, dh/dt = 0. Therefore, the equation becomes:
2x(dx/dt) = 2l(dl/dt)
Now, let's substitute the given values into the equation:
2(30)(dx/dt) = 2(50)(dl/dt)
Simplifying the equation, we get:
30(dx/dt) = 50(dl/dt)
Dividing both sides by 10, we get:
3(dx/dt) = 5(dl/dt)
Now, we know that the rate at which the kite is moving horizontally (dx/dt) is 5 km/h. Substituting this value into the equation, we get:
3(5) = 5(dl/dt)
15 = 5(dl/dt)
Dividing both sides by 5, we get:
3 = dl/dt
Therefore, the rate at which the cord is being released is 3 km/h.
Answer: (c) 3 km/h
- Horizontal distance of the kite from the boy (x) = 30 m
- Length of the cord (l) = 50 m
- Rate at which the kite is moving horizontally (v) = 5 km/h
To find:
The rate at which the cord is being released
Concept:
In this problem, we can use the Pythagorean theorem to relate the horizontal distance of the kite from the boy (x), the length of the cord (l), and the height of the kite (h).
Solution:
Let's assume the height of the kite is h. According to the Pythagorean theorem, we have:
x^2 + h^2 = l^2
Differentiating both sides with respect to time, we get:
2x(dx/dt) + 2h(dh/dt) = 2l(dl/dt)
Since the height of the kite remains constant, dh/dt = 0. Therefore, the equation becomes:
2x(dx/dt) = 2l(dl/dt)
Now, let's substitute the given values into the equation:
2(30)(dx/dt) = 2(50)(dl/dt)
Simplifying the equation, we get:
30(dx/dt) = 50(dl/dt)
Dividing both sides by 10, we get:
3(dx/dt) = 5(dl/dt)
Now, we know that the rate at which the kite is moving horizontally (dx/dt) is 5 km/h. Substituting this value into the equation, we get:
3(5) = 5(dl/dt)
15 = 5(dl/dt)
Dividing both sides by 5, we get:
3 = dl/dt
Therefore, the rate at which the cord is being released is 3 km/h.
Answer: (c) 3 km/h
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Community Answer
The horizontal distance of a kite from the boy flying it is 30 m and ...
Since, speed of wind = 5 Km/h
it is passing horizontally for the will be less than the speed of the wind and will be in the same ratio
∴ Required answer = 5km/h
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The horizontal distance of a kite from the boy flying it is 30 m and 50 m of cord is out from the roll. If the wind moves the kite horizontally at the rate of 5 km/h directly away from the boy, how fast is the cord being released?a)3 km/hb)4 km /hc)5 km/hd)6 km/hCorrect answer is option 'C'. Can you explain this answer?
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