# Help with trigonometry question

• Nov 28th 2010, 05:47 AM
lauangela
Help with trigonometry question
Hi, i need help in this trignometry question and i don't quite understand how to solve it this question is dealing with the equation:

y-k sin or cos (x-h)
---- = -----------------
b a

just in case your not sure

k = vertical shift
b = amplitude
h = horizontal shift
a = period

here is the question:

a tire with a diameter of 63 cm coasts at 1.6 m/s over a nail at exactly 12:00 noon. the nail is stuck in the tire but does not deflate

a. how high above the ground will the nail be at:
1. 12:00:08
2. 12:00:15
3: 12:01:00
4: 12:15:00

b. Find the first four times the nail at 10 cm above the ground

thanks! i really need to understand this question
• Nov 28th 2010, 06:18 AM
skeeter
Quote:

Originally Posted by lauangela
Hi, i need help in this trignometry question and i don't quite understand how to solve it this question is dealing with the equation:

y-k sin or cos (x-h)
---- = -----------------
b a

just in case your not sure

k = vertical shift
b = amplitude
h = horizontal shift
a = period

here is the question:

a tire with a diameter of 63 cm coasts at 1.6 m/s over a nail at exactly 12:00 noon. the nail is stuck in the tire but does not deflate

a. how high above the ground will the nail be at:
1. 12:00:08
2. 12:00:15
3: 12:01:00
4: 12:15:00

b. Find the first four times the nail at 10 cm above the ground

thanks! i really need to understand this question

the first thing you need to determine is the period of up and down motion for the nail.

$\omega = \frac{v}{r} = \frac{160 \, cm/s}{31.5 \, cm} = \frac{320}{63} \, rad/s$

period, $T = \frac{2\pi}{\omega} = \frac{63\pi}{160} \approx 1.24 \, s$

at $t = 0$, the nail is on the ground and rises to a height of 63 cm at $t = \frac{63\pi}{320} \approx 0.62 \, s$

since the cycle starts at a low point (h = 0) , goes up to a height of h = 63 cm and back down, a negative cosine curve is probably the best model to simulate the motion of the nail up and down over time.

$h = -31.5 \cos\left(\frac{320}{63} \cdot t\right) + 31.5$

where h is height above the ground in cm and t is time in seconds.
• Nov 28th 2010, 06:38 AM
lauangela
thanks for the reply but i am still very confuse about the whole thing

1. 12:00:08
2. 12:00:15
3: 12:01:00
4: 12:15:00

how high?

im sorry but i'm just confuse by the whole work

i need to identify the periods, amplitude, horizontal and vertical shift but then i can't see it and overall confuse
• Nov 28th 2010, 06:44 AM
skeeter
Quote:

Originally Posted by lauangela
thanks for the reply but i am still very confuse about the whole thing
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "http://mathhelpforum.com/trigonometry/164598-help-trigonometry-question-print.html", "fetch_time": 1495607699000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2017-22/segments/1495463607802.75/warc/CC-MAIN-20170524055048-20170524075048-00572.warc.gz", "warc_record_offset": 236534119, "warc_record_length": 3527, "token_count": 836, "char_count": 2655, "score": 4.21875, "int_score": 4, "crawl": "CC-MAIN-2017-22", "snapshot_type": "longest", "language": "en", "language_score": 0.9001593589782715, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00031-of-00064.parquet"}