P(t) models the distance of a swinging pendulum (In CM) from the place it has...

Kendall Holder

Kendall Holder

Answered

2022-01-23

P(t) models the distance of a swinging pendulum (In CM) from the place it has travelled t seconds after it starts to swing. Here, t is entered in radians.
P(t)=5cos(2πt)+5
What is the first time the pendulum reaches 3.5 CM from the place it was released?
Round your final answer to the hundredth of a second.
Ok, so I did this to get the solution:
3.5=5cos(2πt)+5
1.5=5cos(2πt)
0.3=cos(2πt)
cos1(0.3)=2πt
cos1(0.3)2π=t
The fact is this gives me 11.55 seconds to get to 3.5 CM, which does not sound right. Where did I go wrong and how can I fix it?

Answer & Explanation

Fallbasisz8

Fallbasisz8

Expert

2022-01-24Added 9 answers

Obviously you're expecting the input to cos in radians because you have 2π  in  cos(2πt). In physics you always use radians.
However, you can get it to work in degrees with a slight modification: change 2π to 360. Don't make it a habit though. Stay away from degrees.

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