Because of friction and air resistance, each swing of a pendulum is a little shorter than the previous one. The lengths of the swings form a geometric sequence. Suppose the first swing of the pendulum has an arc length of 100cm and a return swing of 99cm.

a.) On which swing will the length first have a length less than 50 cm?

b.) Find the total distance traveled by the pendulum until it comes to rest.

Question

Because of friction and air resistance, each swing of a pendulum is a little shorter than the previous one. The lengths of the swings form a geometric sequence. Suppose the first swing of the pendulum has an arc length of 100cm and a return swing of 99cm.

a.) On which swing will the length first have a length less than 50 cm?

b.) Find the total distance traveled by the pendulum until it comes to rest.

anonymous · Answer

@jim_thompson5910

anonymous · Answer

I know the answers but I want to see how they got them.

anonymous · Answer

a: 70th swing
b: 10,000 cm

jim_thompson5910 · Answer

you would use the formula

an = 100*(0.99)^(n-1)

plug in an = 50 to get

50 = 100*(0.99)^(n-1)

then solve for n

jim_thompson5910 · Answer

this is all for part a

jim_thompson5910 · Answer

for part b), you use the formula

S = a/(1-r)

anonymous · Answer

can you show me step by step so ikno i wrote it right? pleasee!

anonymous · Answer

@jim_thompson5910

anonymous · Answer

?? @jim_thompson5910

jim_thompson5910 · Answer

50 = 100*(0.99)^(n-1) 

50/100 = (0.99)^(n-1) 

0.5 = 0.99^(n-1)

log(0.5) = log(0.99^(n-1))

log(0.5) = (n-1)log(0.99)

log(0.5)/log(0.99) = n-1

I'll let you finish

anonymous · Answer

Did you ever get the rest of this?
@jim_thompson5910 Could you finish this so I can check my answer?