Problema Solution
A person flying a kite holds the string 5 feet above ground level, and the string is payed out at a rate of 2 ft/sec as the kite moves horizontally at an altitude of 105 feet. Assuming there is no sag in the string, find the rate at which the kite is moving when 125 feet of string is payed out.
Answer provided by our tutors
Picture a triangle formed in the air by the string of the kite and the person flying the kite. The kite stays at a constant 100 feet above the person(remember, it's 5 feet off the ground). The string is 125 feet and moving out at 2 ft/sec.
So, identify what we have:
y=105 - 5 = 100 ft
z=125 ft
dz/dt=2 ft/sec
by using Pythagorean Theorem, we find x
x^2 + 100^2 = 125^2
x = 75
click here to see the step by step solution of the equation
We want to find dx/dt
we already know
z^2=x^2+y^2
Differentiate
2z(dz/dt) = 2x(dx/dt) + 0
dx/dt = (z/x)(dz/dt)
dx/dt = (125/75)*2
dx/dt = 10/3 ft/sec
dx/dt = 3.33 ft/sec
When 125 feet of string have been paid out, the kite is moving horizontally at 3.33 ft/sec.