Aspring with a force constant of 5100 n/m and a rest length of 2.6 m is used in a catapult. when compressed to 1.0 m, it is used to launch a 48 kg rock. however, there is an error in the release mechanism, so the rock gets launched almost straight up. how high does it go (in m)? (assume the rock is launched from ground height.) m how fast is it going (in m/s) when it hits the ground? m/s

First let’s find the total force exerted on the rock.
Fs=1/2kx^2= 1/2*5100*(1.6)^2=6528N
Then setting it equal to U=mgh and solving for h we get h=6528N/(9.8m/s^2*48kg)= 13.9m

Then using K=1/2mv^2 we can solve for the final velocity of the rock.
(6528N*2)/48kg then taking the sqrt of that we get Vf= 16.5m/s

Acetic acid  /əˈsiːtɪk/, systematically named  ethanoic acid  /ˌɛθəˈnoʊɪk/, is a colourless liquid  organic compound  with the  chemical formula  ch3cooh (also written as ch3co2h or c2h4o2). when undiluted, it is sometimes called  glacial acetic acid.  vinegar  is no less than 4% acetic acid by volume, making acetic acid the main component of vinegar apart from water. acetic acid has a distinctive sour taste and pungent smell. in addition to household vinegar, it is mainly produced as a precursor to  polyvinyl acetate  and  cellulose acetate. it is classified as a  weak acid  since it only partially  dissociates  in solution, but concentrated acetic acid is corrosive and can attack the skin.acetic acidnamespreferred iupac nameacetic acidsystematic iupac nameethanoic acidother namesvinegar (when dilute); hydrogen acetate; methanecarboxylic acid[1][2]identifierscas number64-19-7  3d model (jsmol)interactive image3dmetb00009 reference506007chebichebi: 15366  chemblchembl539  chemspider171  drugbankdb03166  echa infocard100.000.528ec number200-580-7e numbere260  (preservatives)gmelin reference1380iuphar/bps1058keggd00010  meshacetic+acidpubchem  cid176rtecs numberaf1225000uniiq40q9n063p  un number2789inchiinchi=1s/c2h4o2/c1-2(3)4/h1h3,(h,3,4)  key:   qtbsbxvteameqo-uhfffaoysa-n  smilescc(o)=o