A Ferris wheel is 115 feet in diameter and rises 125 feet off the ground. Each r

Question

A Ferris wheel is 115 feet in diameter and rises 125 feet off the ground. Each revolution of the wheel takes 30 seconds.

1.What is the angular speed of the wheel?

2.Express the height h of a passenger off the ground as a function of t if t=0 corresponds to the time when a passenger is at the bottom.

A mass suspended from a spring is stretched 6.5 cm from its equilibrium position and then released. The mass then displays damped harmonic motion with period pi. After 10.995 seconds, the amplitude of motion is observed to be 1.24926100051846 cm. Find a formula of the form y(t) = A e^{-kt} cos(omega t) to model the motion of the mass.

1. K=

2.W=

3.Y=

Explanation / Answer

1)

diameter =115 ft

=> radius ,r=115/2=57.5 ft

period = 30seconds

=>angular speed =2/30 =(/15) radians/second

average height =(125-115) +(57.5) =67.5

height h of a passenger off the ground as a function of t is , h(t)= - 57.5cos((/15)t) +67.5

======================================

2)

period =

=>2/w =

=>w=2

A=6.5

y(10.995) = 1.24926100051846

=>6.5e(-k*10.995)= 1.24926100051846

=>e(k*10.995)=(6.5/1.24926100051846)

=>10.995k =ln(6.5/1.24926100051846)

=>k=(1/10.995)ln(6.5/1.24926100051846)

=>k=0.15

1. k=0.15

2.w=2

3.y=6.5e(-0.15t)cos(2t)

please rate if helpful. please comment if you have any doubt

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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