Venus is a grade 12 learner and she claims that she can shoot a stone 50m vertically high by using a catapult.She wants to know the relationship between the height reached by the stone and the initial velocity of it.
Assuming the stone is to be hurled vertically with velocity v,
h(t) = vt - 4.9t^2
h will reach maximum height at t=v/9.8 seconds. So, the max height H is
H(v) = v(v/9.8) - 9.8/2 * (v/9.8)^2
= v^2/9.8 - (v^2/9.8)/2
= v^2/19.6