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For the next point I will discuss elements of what to carry for a day hike.
1.A small rucksack 15 or 20l, a padded back is a bonus but not necessary
2.Water, in bottles, canteens or bladders of choice, the amount consumed varies following terrain and weather; for a 10h hike about 4 liters should be consumed at minimum in order to stay hydrated, make sure to plan resupply or carry it with a little extra.
Do not drink large amounts at once, do not wait to get very thirsty, two or three small sips of about 3dl total every 15 minutes will prevent cramps and keep proper hydration. Overweight people will get significantly more thirsty. Do not drink from suspicious sources.
3.Food, some salty to keep electrolytes balanced, such as sandwiches with relatively fatty stuffing, and some sweet to keep up energy, chocolate is perfect in that regard.
Do not carry foods you would not normally eat in order to avoid digestion issues.
4.Waterproof jacket or poncho, the latter can also cover the rucksack and will provide much better ventilation, it might be unsuitable in strong wind.
A sweater or jumper, depending on the region even during summer.
5.For longer hikes, a small fist aid kit containing at minimum few bandaids, a couple pieces of gauze, a bandage, an elastic bandage for ligaments, a mylar blanket, tweezers, small scissors and disinfectant wipes. Content varies following location. Have an idea on its usage.