Trunks concludes that Vegeta is strong enough to handle the attack.  Unfortunately, he was dead wrong.   Piccolo's ki blast slams Vegeta, and for some reason, he is unable to block it.   "What...is this!", questions Vegeta.  "You fool!  I told you, I am now the strongest in the universe and no one can stop me!", Piccolo gloats.   Right then, Piccolo delivers the death blow by flying up to him and launching a ki blast right against Vegeta's head.  That finishes up the mighty Saiyajin instantly.   "NOOOOOOOOOO!!!  DAD!", Trunks yells in horror.  Trunks can't believe his eyes.  Vegeta....defeated by...Piccolo.  No, that can't be!   But it is.  Trunks knows he has just enough power to maybe take out Piccolo, or he can escape while he has the chance so he can tell the Z-Gang what happened to Vegeta.  What should he do?

Take Piccolo out now?

Forget about fighting.  Go home and grieve over your father's death.