1. The science teacher at school wants to build a sundial and has asked for your
ID: 3003869 • Letter: 1
Question
1. The science teacher at school wants to build a sundial and has asked for your help building it in exchange for extra credit. After some research on the Internet, you find the sundial really only needs two parts: some sort of pin to make a shadow, and something with marks on it to tell how long the shadow is. You realize this can be done easily on the sidewalk outside of the school using some floor paint to make markings and an aluminum pin to make the shadow. In the image below at 2:00 the sun is at a 60° angle of inclination. The sun is at 45° at 3:00, and so on 12:00 11:00 1:00 10:00 2:00 9:00 3:00 8:00 4:00 7:00 5:00 6:00 am 6:00 pm h-height of pin 1- length of shadow So, you drill a hole in the sidewalk and push the pin into it. The height (h) of the pin above the sidewalk is the day of the month when you were born. For example, my birthday is the 22nd of the month, so the height of my pin is 22 cm above the sidewalk. You may also choose any number between 1 and 31 if you choose. Here are your tasks for this exploration: a. Assign a value to (h) and state the height of your pin. b. You would need to paint marks on the sidewalk to demonstrate what time it is. Use your knowledge of the trig ratios to determine where to draw the marks on the sidewalk. b. What time of day is the sundial most or least accurate? Why? C. Suppose the sidewalk has 150 meters on either side of the pin where the shadow can appear. At what time in the evening will the shadow run out of sidewalk?Explanation / Answer
a) My birthday is on 8th November. So h=8cm above sidewalk.
b)In order to paint marks first we need to which direction is west accurately. This direction is 6:00 am mark since shadow casts on west side in morning due to sunrise in east.
Similarly east is taken 6:00 pm which is direct opposite of 6:00 am mark. Now we have to draw a semi circle of convenient radius in clockwise direction from 6:00 am mark to 6:00 pm mark.Now for calibration part.
Using a protractor project all the mutliples of 15 on the semicircle
After that draw a line between 6:00 am and 6:00pm line and project all points on semicircle on this line using a ruler.
c) Sundial is least accurate in afternoon since the lenght of shadow is too short
d)From above picture l=tan(theta)h
given l=150 cm ,h=8cm
which implies theta=86.94 degrees
for 75degrees its reaches 5:00pm
remaining 11.94=12(approx)degrees are added as minutes when they are mutliped by 4. Hence the time would be 5:48pm or 6:12am(doing similarly on left side) when the shadow breaks out of sidewalk.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.