The Giant Soup Can of Hornby Island puzzle

The actual dimensions of a Campbell's Soup can are approximately 51 cm in height and 41 cm in width. Comparatively, the bike's height is around 110 cm. Upon examining the photo, it appears that the tank's height or width is approximately 2.5 times that of the bike, which suggests a measurement of roughly 275 cm. Taking into account the ratio of height to width found in the can, we can estimate the tank's length to be approximately 342 cm. With these dimensions in mind (342 cm in height and 275 cm in width), we can calculate the tank's volume using the formula for the volume of a cylinder, yielding a value of approximately 20.3 cubic meters. It's worth noting that, on average, around 3,000 gallons of water are used during a house fire. Converting this amount to approximately 11.4 cubic meters, we can conclude that the estimated tank volume of 20.3 cubic meters would be sufficient for firefighting purposes.

My own puzzle:
You're out for a walk in the afternoon when you notice an interesting pattern of sunlight and shadows being cast by a tree and a lamppost. You observe that the shadow of the tree and the shadow of the lamppost meet at a certain point on the ground. 
Given: 
The height of the tree is 4 meters.
The height of the lamppost is 2 meters.
The distance between the base of the tree and the base of the lamppost is 6 meters.
The angle of elevation of the sun is 45 degrees.
Question 1:
Calculate the length of the shadow cast by the tree?
Question 2:
Calculate the length of the shadow cast by the lamppost?
Question 3:
Where do the shadows of the tree and lamppost meet on the ground, and how far is it from the base of the tree?






Comments

  1. Susan GerofskyNovember 12, 2023 at 6:39 PM

    What a lovely extension problem, and a really beautiful photo that inspired it, Sheng! Very interesting. Good solution for the soup can problem as well.

    ReplyDelete

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