Math  /  Calculus

QuestionAt least one of the answers above is NOT correct.
A street light is at the top of a 22 ft pole. A 6 ft tall girl walks along a straight path away from the pole with a speed of 5ft/sec5 \mathrm{ft} / \mathrm{sec}. At what rate is the tip of her shadow moving away from the light (ie. away from the top of the pole) when the girl is 40 ft away from the pole? Answer: (118)2[40222+(118)2+402(5)\left(\frac{11}{8}\right)^{2}\left[\frac{40}{\sqrt{22^{2}+\left(\frac{11}{8}\right)^{2}+40^{2}}}(5)\right.
How fast is her shadow lengthening? Answer: 158\frac{15}{8}
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Studdy Solution
Pour trouver la vitesse à laquelle le bout de l'ombre s'éloigne du lampadaire, nous devons ajouter la vitesse de la fille à la vitesse à laquelle la longueur de l'ombre augmente.
dzdt=dxdt+dydt=5+158=408+158=558\frac{dz}{dt} = \frac{dx}{dt} + \frac{dy}{dt} = 5 + \frac{15}{8} = \frac{40}{8} + \frac{15}{8} = \frac{55}{8}
Ainsi, la vitesse à laquelle le bout de l'ombre s'éloigne du lampadaire est 558\frac{55}{8} pieds par seconde.
La solution est :
La vitesse à laquelle le bout de l'ombre s'éloigne du lampadaire est 558\frac{55}{8} pieds par seconde.
La vitesse à laquelle la longueur de l'ombre augmente est 158\frac{15}{8} pieds par seconde.

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