A kite 75ft above the ground moves horizontally at a speed of 6ft/s. At what rat

Question

A kite 75ft above the ground moves horizontally at a speed of 6ft/s. At what rate is the angle between the string and the horizontal decreasing when 150ft of string has been let out? answer (in radians per second): The length of a rectangle is increasing at a rate of 6cm s and its width is increasing at a rate of 5cm s. When the length is 40cm and the width is 20cm. how fast is the area of the rectangle increasing? answer (in cm^2, s) A street light is at the top of a 18 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 feet from the base of the pole? The tip of the shadow is moving at ft/sec.

Explanation / Answer

(1A)so we have, sin = opp / hyp = 75/150 = 1/2
therefore, = 30 degree
now horizontal distance travelled by the kite (again assuming the person flying the kite is still/not moving) or adjacent side = cos x hypotenuse = (cos 30degree) x 150 ft = 129.9 ft
time elapsed so far = distance / speed = 129.9 ft / (6 ft/s) = 21.65 secs
so, rate at which angle is decreasing = total angle covered / time elapsed = 30 degree/21.65 = 1.385 degrees / sec

(1B) Area=A =lb

=> dA/dt=l*db/dt+b*dl/dt=40*5+20*6=200+120=320 cm^2/s

(1C)Let x be the distance between the woman and the pole,
y be the distance between the woman and the shadow tip.
then
(x+y)/18=y/6
=>(x+y)/y=3
=>y/x=1/3
=>(xdy/dt-ydx/dt)/x^2=0
=>(45dy/dt-(1/3)*45*4)/45*^2=0
=>dy/dt=15*4/45=4/3 ft/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.