Water balloon is thrown upward from balcony so that height in feet above the ground is given by s= -16t^2 +24t +30

Question

Water balloon is thrown upward from balcony so that height in feet above the ground is given by s= -16t^2 +24t +30 where t is the number of seconds since the balloon was released. 

a.)when will the water balloon hit the ground?

 

b.) what will the maximum height of the water balloon?

Answer 1

(a)

 

Set s(t) = 0 and solve the resulting quadratic equation for t.  It will give a positive and a negative solution.  Since time starts at t = 0 at the moment of launch, discard the negative solution; keep only the positive solution.

 

(b)

 

Maximum height occurs at the vertex of the height vs. time parabola, which is at

 

t = -24/[2(-16)] seconds = 0.75 seconds

 

Evaluate s(0.75), and that will give maximum height.

 

h_max = s(0.75)