#03 Cube Shadow
At midday at her home in Ecuador, Natalia holds a solid cube 1 metre above the ground and it casts a shadow. She rotates the cube a bit and finds that the smallest shadow she can create is a square. What is the shape of the largest shadow she can produce with the cube at noon and how much bigger is it than the square shadow?
Answer next week
#02 Getting past the freight train Solution
We asked how a long passenger train could get past a freight train pulling three wagons on a single track line with a siding that holds two wagons.
The freight train (FT) detaches the back two trucks, then drives into the siding. The passenger train (PT) now pushes the two trucks beyond the siding, and the FT with one truck reverses out of the siding and out of the way so that the PT can pull the two trucks back and then push them into the siding before heading down the line again.
Next, the FT pulls the trucks out of the siding and pushes them behind the PT. The FT then reverses and goes into the siding with its one truck. The PT pushes the other two trucks back up the line, and can then head off down the track unimpeded. The FT reverses out of the siding to pick up its other two trucks.
Incidentally, it is always possible for the PT to pass the FT however many trucks the FT has 鈥� but the number of steps increases.
Quick quiz #03
1 What name is given to different physical forms of the same chemical element, for example diamond and graphite in the case of carbon?
2 鈥淣ow I am become death, destroyer of worlds.鈥� With which physicist, wartime head of Los Alamos National Laboratory, is this quotation associated as he watched the first nuclear bomb detonate in July 1945?
3 Clocking just 1268 hours of sun in 2016 鈥� 3.5 hours a day 鈥� what is Europe鈥檚 least sunny capital city?
4 Which Tanzanian gorge is famed for its many discoveries of hominin fossils?
5 When an Italian astronomer gave a Dutch polymath a ride in 1997, where did the two end up eight years later?
Answers below
Answers
1. Allotropes
2. J. Robert Oppenheimer
3. Reykjavik, Iceland
4. Olduvai
5. Saturn and Titan. The Cassini probe, named after Giovanni Domenico Cassini, orbited the ringed planet, while the piggybacking Huygens lander, named after Christiaan Huygens, descended to its largest icy moon
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