Story problem help please! Thanks!

Question

An object is projected vertically upward with an initial velocity of v0 ft/sec, and its distance s(t) in feet above the ground after t seconds is given by the formula s(t) = −16t2 + v0t.
(a) If the object hits the ground after 10 seconds, find its initial velocity v0.
v0 = ??? ft/sec

(b) Find its maximum distance above the ground.
s(t) = ???ft

Answer 1

(a)  Set s(t)=0 and t=10.  Solve the resulting linear equation for v₀.  

 

(b)  The vertex of a parabola in the form s(t) = at^2 + bt + c occurs where t = -b/(2a).  Since a<0 the vertex will be the maximum value.  Evaluate s(t) with t = -b/(2a).