Derek kicks a soccer ball off the ground and in the air with an initial velocity of 31 feet per second. Using the formula H(t) = −16t2 + vt + s, what is the maximum height the soccer ball reaches?

14.2 feet

14.6 feet

15.0 feet

15.3 feet

Question

Derek kicks a soccer ball off the ground and in the air with an initial velocity of 31 feet per second. Using the formula H(t) = −16t2 + vt + s, what is the maximum height the soccer ball reaches?

 14.2 feet

 14.6 feet

 15.0 feet

 15.3 feet

anonymous · Answer

i think it's 15.0 feet

hero · Answer

How do you know this? Did you do any calculations to figure that out?

anonymous · Answer

yes

hero · Answer

Show me what you've done.

anonymous · Answer

H(t) = -16t^2 + 31t = -t(16t - 31) 
At the maximum height, t = (1/2)(0+31/16) = .96875
H( .96875) = 15.0 ft

hero · Answer

What happened to the + s part of the formula?

anonymous · Answer

oh

anonymous · Answer

H(t) = −16t^2 + vt + s
dH(t)/dt = −32t + v 
0 = −32t + 31
t = 31/32

anonymous · Answer

substitute into H(t) = −16t^2 + vt + s

anonymous · Answer

s is unknown

hero · Answer

If s is not known, you need to figure out what its value is. You can't just ignore it.

anonymous · Answer

oh ok

anonymous · Answer

well thats where i got stuck on