A kite is flying at a height of $3 \text{ m}$ and $5 \text{ m}$ of string is out. If the kite is moving away horizontally at the rate of $200 \text{ cm/s}$, find the rate at which the string is being released.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $160 \text{ cm/s}$ ##
Using the Pythagorean theorem:
$x^2 + 3^2 = y^2$
When $y = 5$ then $x = 4$, now $2x \frac{dx}{dt} = 2y \frac{dy}{dt}$
$4(200) = 5 \frac{dy}{dt} ⇒\frac{dy}{dt} = 160 \text{ cm/s}$