Question 461455
the "little o" is for "v zero" (the velocity at time zero, or initial velocity)


using the parabola that describes the trajectory, solve for the zeros (roots)
___ one root will be the starting (launch) point, and the other root will be the end point (range)
___ h(x) equals zero at the beginning and the end of the projectile flight


0 = -0.005x^2 + x ___ factoring ___ 0 = x(-0.005x + 1)


0 = x ___ this is the launch


0 = -0.005x + 1 ___ 0.005x = 1 ___ x = 200 ___ this is the range



the maximum height of the projectile occurs at the vertex of the parabola, on the axis of symmetry
___ the general equation is ___ x = -b / (2a)


in this case ___ x = -1 / [2(-0.005)] ___ x = 100 (this is half the range, as would be expected)
___ use this x-value to find the max height


h(100) = -0.005(100)^2 + (100) ___ h(max) = -50 + 100 ___ h(max) = 50