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1.
when one person offers to make fuck with another because the first person hasn't gotten any in a really long time; results from "feeling bad" about the other person not getting any
"I'm in the mood to give you a mercy jump. Time to break you out of that slump!"
by Eric Loy April 13, 2004
 
2.
A sexual encounter in which one individual is clearly "taking one for the team" to elevate his friends chance of getting laid. Or A sexual encounter derived purely from sympathy.
Jodi is a 40 year old woman who has 3 kids and works all the time she needs a mercy jump.

I know she's a little chubby, but can you give my girlfriend's sister a mercy jump.
by Rob Williams13 January 03, 2008