The footage played at Hull Crown Court showed Jamie Nickell, 26, land feet first on the tent in a shop doorway on Whitefriargate in the city centre as his friend Jake Mann filmed him on a phone.
A judge was told that one of the defendants was heard to shout: "You dirty, scumbag, trampy b*******."
Nickell, from Lincoln, admitted assault causing actual bodily harm to one of the men in the tent - Steven Cadman, who suffered a minor injury to his knee.
Sentencing Nickell to four months in prison, Judge Mark Bury said: "What you did is repugnant to right-minded people.
"There are too many homeless people in our society these days.
"They do not need to be treated in this way.
"The way you treated them is such that only an immediate sentence of imprisonment is justified."
Judge Bury said he accepted that Nickell was ashamed of what he did, noting that the defendant could not bring himself to look at the footage when it was played in court.
But he said: "Homelessness is not a lifestyle choice, it is a necessity, unhappily, for some members of our society. It is corrosive of their well-being and their state of mind.
"They ought to be treated with a degree of understanding and sympathy."
Julia Baggs, defending, said: "Mr Nickell is utterly disgusted and appalled by his behaviour."
She said: "His behaviour was mean, it was thoughtless. He is thoroughly ashamed and embarrassed about what he did.
"Mercifully there were no significant injuries caused."
Ms Baggs said her client is a valued worker for a construction and landscaping firm and supports two very young daughters, who live with their mother.
He has one previous conviction for pushing a doorman, she said.
Earlier this week, the same judge jailed Mann, 29, also from Lincoln, for 14 weeks for his part in the attack, which happened on November 30 last year.
The judge heard how the pair were drunk after travelling to Hull to go to a concert.