contestada

A Ferris wheel with a radius of 13 m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when the rider is 18 m above ground level?

Respuesta :

assume the center of ferris wheel is 13 m from ground 
h = elevation of rider 
A = angle of elevation of rider with respect to center of ferris wheel 
dA/dt = 2pi/2 = pi rads/min 

h = 13sin(A) + 13 

dh/dt = 13cos(A)dA/dt 

when h = 18 m 
18 = 13sin(A) + 13 
sin(A) = 5/13 
cos(A) = sqrt(1 - (5/13)^2) 
cos(A) = 12/13 

dh/dt = 13*12/13*pi 
dh/dt = 12pi m/min

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