This should be .

What? a ball is thrownso at t=10/g, i get s= 5.1upwardfrom the top of a 100 m building and you assert that its highest point it 5.1 m??

What value did you use for g? 9.8? . If you are calculating "height above the building" then your "K" is 0.

Did they really set that equal to v? From your , . Put that into and you get . Multiply both sides by 2g to get which is the same as , not v.this answer is correct but they use

can anyone show me how they got this equation?

You can also interpret that in terms of energy. At velocity v, the kinetic energy is and at height the potential energy is . Multiply both sides of by m/2 and you have or - that the total energy, kinetic energy plus potential energy, at any point is equal to the kinetic energy at the start where the potential energy was 0.

a= -g doesn't it? so that v= -gt+ v1?For part b) they want the time taken to go from h=50 to h=0.

for this i used the formula above for s and solved for t wneh h-50 and 0 to get the correct answer.

in the solutions they use

and if v2 is velocity at H=0 and v1 is velocity at H=50 then

v2=v1-gt

is the above obvious?im thinking,wrongly, if i start motion at v1 then f=ma gives me a=g so v=gt+K but initially v=v1 thus v=gt+v1 ??

Yes, that's what I just said: v= -gt+ v1 is the same as v2= v1- gt.Can i get v2=v1-gt starting with f=ma?