Question #b6d23

1 Answer
May 16, 2016

25%

Explanation:

If we define the initial velocity as having magnitude uu, then the vertical component of this is u*sin30usin30 (the horizontal component would be u*cos30ucos30 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 ss upwards. At this point its vertical velocity will be nil. We can used the following to determine ss:
v^2=u^2+2asv2=u2+2as
We know vv, final velocity is nil, and uu, initial velocity is usin30usin30 and aa will be acceleration due to gravity, gg (which will be negative relative to the direction of the initial velocity). Hence:
0=u^2sin^2 30-2gs0=u2sin2302gs
2gs=u^2sin^2 302gs=u2sin230
s=(u^2sin^2 30)/(2g)s=u2sin2302g

So final potential energy will be:
PE=mgh=mgsPE=mgh=mgs

PE=(mg)*(u^2sin^2 30)/(2g)PE=(mg)u2sin2302g

PE=(m*u^2sin^2 30)/(2)PE=mu2sin2302

Initial kinetic energy is
KE=1/2m*u^2KE=12mu2
So percentage conversion is:

"PE"/"KE"=(m*u^2sin^2 30)/(2)/(1/2m*u^2)PEKE=mu2sin2302/(12mu2)

"PE"/"KE"=sin^2 30=0.25PEKE=sin230=0.25
So the answer is 25%