Question

A kite glides horizontally at an altitude of 20 m while we unspool the string. Consequently, the angle made between the string and the horizon diminishes. We would like to determine the rate at which this angle decreases once 50 m of string has been unspooled, given that, at that instant, the kite's horizontal velocity is 1 m/s. To solve this problem, let ? be the angle in radians made between the string and the horizontal, x the kite's horizontal position in meters since being attached to the ground, and t the time in seconds. We further suppose that the string is straight and taut. (a) Sketch a diagram of this question and use it to express ? as a function of x . ? = rad (b) What is the value of x at the moment in question? Give the exact value. x = m (c) What is the value of d?/dt at the same moment? Give the exact value, paying attention to the sign. d?/dt = rad/s

          A kite glides horizontally at an altitude of 20 m while we unspool the string. Consequently, the angle made between the string and the horizon diminishes. We would like to determine the rate at which this angle decreases once 50 m of string has been unspooled, given that, at that instant, the kite's horizontal velocity is 1 m/s.

To solve this problem, let ? be the angle in radians made between the string and the horizontal, x the kite's horizontal position in meters since being attached to the ground, and t the time in seconds.

We further suppose that the string is straight and taut.

(a) Sketch a diagram of this question and use it to express ? as a function of x .

? =
rad

(b) What is the value of x at the moment in question? Give the exact value.

x =
m

(c) What is the value of d?/dt at the same moment? Give the exact value, paying attention to the sign.

d?/dt =
rad/s

A kite glides horizontally at an altitude of 20 m while we unspool the string. Consequently, the angle made between the string and the horizon diminishes. We would like to determine the rate at which this angle decreases once 50 m of string has been unspooled, given that, at that instant, the kite's horizontal velocity is 1 m/s.

To solve this problem, let ? be the angle in radians made between the string and the horizontal, x the kite's horizontal position in meters since being attached to the ground, and t the time in seconds.

We further suppose that the string is straight and taut.

(a) Sketch a diagram of this question and use it to express ? as a function of x .

? =
rad

(b) What is the value of x at the moment in question? Give the exact value.

x =
m

(c) What is the value of d?/dt at the same moment? Give the exact value, paying attention to the sign.

d?/dt =
rad/s

Added by Kenneth M.

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