The dumb people are running the world, while the smart people are their assistants and secretaries and such. The dumb people find that their planet is dying or threatened. The smart people build a space craft to take them to a new planet. Only the ship launches and then crash lands (on purpose) into a body of water.
You don't specify if this is a book, film, or TV show but this corresponds very well with segment of Douglas Adams Hitchhikers Guide to the Galaxy stories involving the Golgafrincham ArK Fleet which is comprised of "the useless third of the population" When their planet is endangered this portion of the population is put on a spaceship and programmed to deliberately crash on another planet to get rid of them. This story exists in a number of formats, Radio series, novel BBC TV series and a film. Here are the clips from the TV series.
The canonical SF story that deals with a world dominated by the stupid, with the intelligent suffering as effectively their servants, leading to the bulk of the population being sent to another planet to die is "The Marching Morons," by C. M. Kornbluth, probably the author's best known and most influential work. While the story described in the question has some different features, the main plot element seems to be the same.
The plot summary, per Wikipedia:
The human population is now 3,000,000 highbred elite and 5,000,000,000 morons, and the "average" IQ is 45 (whereas now an IQ score of 100 is average, by definition). Several generations before the onset of the story, the small number of remaining 100-and-higher-IQ technocrats work feverishly to keep the morons alive.
The elite have had little success in solving the Problem (also called "Poprob", for 'population problem', in the story) for several reasons:
The morons must be managed or else there will be chaos, resulting in billions of deaths and "five hundred million tons of rotting flesh";
It is not possible to sterilize all of the morons;
- Propaganda against large families is insufficient, because every biological drive is towards fertility (the story predates the development of hormonal contraception).
The elite have tried everything rational to solve the population problem but the problem cannot be solved rationally. The solution requires a way of thinking that no longer exists – Barlow's "vicious self-interest" and his knowledge of ancient history.
Barlow derives a solution based on his experience in scamming people into buying worthless land and knowledge of lemmings' mass migration into the sea: convince the morons to travel to Venus in spaceships that will kill their passengers out of view of land. The story predates the moon landing, and the safety of space travel is summed up in a description of a rocket that crashed on the moon. Propaganda depicts Venus as a tropical paradise, with "blanket trees", "ham bushes" and "soap roots". In a nationalistic frenzy, every country tries to send as many of their people to Venus as possible to stake their claim.
The full text is available online via Project Gutenberg.