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 limit as it depends on the direction of wind and phase of flight. A crosswind above about 40mph and tailwind above 10mph can start to cause problems and stop commercial jets taking off and landing.
A plane flying into Leeds Bradford Airport in the United Kingdom today nearly didn't make it, as incredibly strong winds blew the aircraft nearly sideways. The aircraft survived 60 mph gusts by approaching the runway from a side angle, its skilled pilots managing to narrowly make it onto the runway.
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.
Expect to see many pilots divert in winds much above 40 knots even if the airport is open, especially if gusting to above 50. Crosswinds are a little different as they depend on the braking action - basically how grippy the runway is.