What is tarzan's speed vf just before he reaches jane? express your answer in meters per second to two significant figures?

Before swinging, T has only potential energy, (no speed)
Ui = mgh
Where h is the vertical displacement of T
From the laws of geometry,
cos45 = (L-h)/L
cos45 = 1-h/L
h/L = 1-cos45
h = L(1-cos45)

Therefore
Ui = mgL(1-cos45)

Proceeding the same way,
Twill raise to aheight of h' due to swing
h' = L(1-cos30)
The PE of T after swing is
Uf = mgh'
Uf = mgL(1-cos30)

Along with the PE , T has some kinetic energy results due to the moment.
Tf = 0.5*mv^2

According to the law of conservation of energy,
Ui = Uf+Tf
mgL(1-cos45) = mgL(1-cos30) + 0.5*mv^2
gL(co30-cos45) = 0.5*v^2
9.8*20*(co30-cos45) = 0.5*V^2
v = 7.89 m/s

The speed f T after swing is 7.89 m/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

Kinetic energy = 1/2mv^2. since the mass is constant we can form a ratio of it's kinetic energy at 60 divided by that at 30 to see ke(60)/ke(30) = +(60^2)/30^2). this may be said to 300% increase.