A kite flies horizontally at an altitude of 20 m while unwinding the rope. Then, the angle that his rope makes with the horizon decreases. We want to determine at what rate this angle decreases when 50 m of rope were unwound knowing that at this moment the horizontal speed of the kite is 1m/s. To solve this problem, we denote by 0 the angle in radians that the chord makes with the horizontal, x the horizontal position in meters of the kite from its attachment to the ground, and t the time in seconds. It is also assumed that the rope is straight and well stretched. (a) Draw a picture and use it to express 0 as a function of x.(rad) (b) What is x at the time in question? Give the exact value.(m) c) What is de/dt at the same time? Give its exact value, paying careful attention to the sign.(rad/s)
A kite flies horizontally at an altitude of 20 m while unwinding the rope. Then, the angle that his rope makes with the horizon decreases. We want to determine at what rate this angle decreases when 50 m of rope were unwound knowing that at this moment the horizontal speed of the kite is 1m/s. To solve this problem, we denote by 0 the angle in radians that the chord makes with the horizontal, x the horizontal position in meters of the kite from its attachment to the ground, and t the time in seconds. It is also assumed that the rope is straight and well stretched. (a) Draw a picture and use it to express 0 as a function of x.(rad) (b) What is x at the time in question? Give the exact value.(m) c) What is de/dt at the same time? Give its exact value, paying careful attention to the sign.(rad/s)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A kite flies horizontally at an altitude of 20 m
while unwinding the rope. Then, the angle
that his rope makes with the horizon
decreases. We want to determine at what rate
this angle decreases when 50 m of rope were
unwound knowing that at this moment the
horizontal speed of the kite is 1m/s.
To solve this problem, we denote by 0 the
angle in radians that the chord makes with the
horizontal, x the horizontal position in meters
of the kite from its attachment to the ground,
and t the time in seconds.
It is also assumed that the rope is straight and
well stretched.
(a) Draw a picture and use it to express 0 as a
function of x.(rad)
(b) What is x at the time in question? Give the
exact value.(m)
c) What is de/dt at the same time? Give its
exact value, paying careful attention to the
sign.(rad/s)
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