2. A body fired vertically up reaches a maximum height of 120 m. The location at which the kinetic energy is 75% of the potential energy is...

Answer 1

For max height : mvₒ²/2 = m•g•H,
Initial velocity
vₒ=sqrt(2•g•H) = sqrt(2•9.8•120)=48.5 m/s.

mvₒ²/2 = mgh + mv²/2,
mv²/2 = mvₒ²/2 – mgh =
=m•g•H -0.75 m•g•H=0.25 m•g•H

mv²/2=0.25mgH
v =sqrt(2•0.25•g•H) = sqrt(0.5•9.8•120)=24.2 m/s.
h =(vₒ²-v²)/2•g =(48.5²-24.2²)/2•9.8=90.1 m.