Green’s Dictionary of Slang

(US) a form of college cheer, rounded off with a cry of sis-boom-bah!, supposedly that of an ascending and exploding rocket.

1860		Vanity Fair (N.Y.) 10 Mar. 164/1: ‘The Skyrocket Cheer’ With his ch-h-h! boom! ah; / Fol-de-rol de riddle-diddle, ch-h-h! boom!! ah!!!
1867		Ball Players’ Chronicle 25 July 2/2: After cheers had been interchanged, and the Nationals had let off a ‘sky rocket’—namely, a sort of finish to three cheers, with a ‘hiss—boom—ah!’—an adjournment was had to the clubhouse [DA].
1890		A.C. Gunter Miss Nobody of Nowhere 65: Pete in one wild moment gives them a deep sepulchral Y!A!L!E! – YALE! suceeded by [...] a Princeton skyrocket. [Ibid.] 123: Augustus [...] dances about and screams out significantly, ‘Skyrockets! Skyrockets!’.
1896		Trenton Eve. Times (NJ) 26 oct. 1/4: The official Princeton cheer is the well-known ‘skyrocket cheer’.
1928		Amarillo Globe-Times (TX) 7 Nov. 1/3: Their cheer leaders [...] led a ‘sky-rocket’ cheer for Hoover.
1933		Oshkosh Northwester (WI) 27 July 8/3: The boys and girls [...] gave Gilbert Anderson a ‘sky-rocket’ cheer.
1947		G.S. Perry Cities of America 222: He is such a stimulating lecturer that many of his classes are preceded by a ‘skyrocket’: a Wisconsin yell reserved for its heroes [DA].
1969		Tampa Bay Times (St Petersburg, FL) 10 June 27/1: Selam has been [...] directing the left field bleacher throng into a roaring ‘sky-rocket’ cheer.