If we define the initial velocity as having magnitude u, then the vertical component of this is u*sin30 (the horizontal component would be u*cos30 but we are not interested in this as it has no effect on potential energy)
A word of caution: there is no definition or reference in the question as to what 30 degrees is measured from; it could be from the horizontal or the vertical. | have assumed from the horizontal. Please let me know if this is not the case and I will re-work.
The body will travel a maximum distance s upwards. At this point its vertical velocity will be nil. We can used the following to determine s:
v^2=u^2+2as
We know v, final velocity is nil, and u, initial velocity is usin30 and a will be acceleration due to gravity, g (which will be negative relative to the direction of the initial velocity). Hence:
0=u^2sin^2 30-2gs
2gs=u^2sin^2 30
s=(u^2sin^2 30)/(2g)
So final potential energy will be:
PE=mgh=mgs
PE=(mg)*(u^2sin^2 30)/(2g)
PE=(m*u^2sin^2 30)/(2)
Initial kinetic energy is
KE=1/2m*u^2
So percentage conversion is:
"PE"/"KE"=(m*u^2sin^2 30)/(2)/(1/2m*u^2)
"PE"/"KE"=sin^2 30=0.25
So the answer is 25%
