Pregunta
A child flies a kite at a height of 90 ft , the wind carrying the kite horizontally away from the child at a rate of
.
How fast must the child let out the string when the kite is 150 ft away from the child?
The child must let out the string at a rate of
when the kite is 150 ft away from the child.
(Simplify your answer.)
How fast must the child let out the string when the kite is 150 ft away from the child?
The child must let out the string at a rate of
(Simplify your answer.)
Ask by Cervantes Fitzgerald. in the United States
Mar 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The child must let out the string at a rate of
when the kite is 150 ft away.
Solución

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Como
Mind Expander
To solve this problem, we can use the Pythagorean theorem. Let
be the horizontal distance from the child to the kite,
be the height of the kite (90 ft), and
be the length of the string. According to the Pythagorean theorem:
Given that the height
is constant at 90 ft, we know that when the kite is 150 ft away from the child,
can be calculated as:
Here, we know the total distance from the child to the kite is 150 ft, so:
Calculating this gives:
Now, we differentiate both sides with respect to time
:
Since the height
is constant,
. Given
, we substitute:
Substituting
ft to find
:
Now we have:
This simplifies to:
Dividing both sides by 300:
Thus, the child must let out the string at a rate of
when the kite is 150 ft away from the child.
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