If a stake is placed in the ground and is 20cm. high and casts a shadow 12.5 cm. long, what time is it? (The sun rises at 6 a.m. and is overhead at noon.)
Major assumption ....
You must be at the equator , or between the two Cancers.
tanØ = 20/12.5 = 1.6
Ø = 57.99 or 58°
The assumption is that the time from 6:00 am to noon, or 6 hours , is proportional to the angle of the sun from 0° to 90°
t/6 = 58/90
t = 6(58/90) = 3.8666..
= 3 hrs and 52 minutes
the time is 9:52 am
To determine the time based on the length of the shadow cast by a stake, we need to make some assumptions and calculations.
First, let's assume that the length of the shadow is proportional to the height of the stake. In other words, if the height of the stake is half, then the length of the shadow will also be half.
Using this assumption, we can set up a proportion to solve for the time:
Height of stake / Length of shadow = Height of the vertical object / Length of shadow at noon
We know that at noon, when the sun is directly overhead, objects cast the shortest shadows. As the sun rises or sets, the angle of the sunlight changes, resulting in longer shadows.
Let's plug in the given values into the equation:
20 cm / 12.5 cm = Height of the vertical object / Length of shadow at noon
Now, to determine the height of the vertical object at noon, we need to know the length of the shadow it casts at that time. However, this information is missing in the question. Without the length of the shadow at noon, we can't calculate the actual time.
So, to answer the question, with the given information (height of stake and length of shadow), it is not possible to determine the exact time.