With this in mind, horizontal winds (also known as “crosswinds”) in excess of 30-35 kts (about 34-40 mph) are generally prohibitive of take-off and landing. As far as how this happens, it depends on where you are in flight.
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There is no single maximum wind speed that cancels flights, as it depends on the direction of wind and phase of flight. A crosswind above about 40mph and a tailwind above 10mph can start to cause problems and stop commercial jets from taking off and landing.
Absolutely. Pretty much any airplane can easily fly in 25 mph winds. If that is a direct crosswind that might make landing smaller aircraft more challenging, but airliners, no problems.
For example, the Boeing 737 has a maximum crosswind landing factor of 30 knots (just over 55 mph). So that answers the second part of your question. Yes, a 'plane can land in 50 mph winds.
The 737 has been designed to withstand landings at 600fpm, reducing to 360fpm at MLW before a hard landing inspection is required. Most pilots report a hard landing when the sink rate exceeds approximately 240fpm.