Question

Help please?! Should be easy!

Answer 1

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

Answer 2

You can always graph the equation, and fine the max value

Answer 3

I have:
H(t) = -16t2 + 31t + s
what goes into s? I am trying to graph it.

Answer 4

diffrentiate H(t) with respect to t keep s as a constant

Answer 5

d{H(t)}/dt=0
calculate t but s will remain unknown in the final equation after substituting t

Answer 6

I think s is your initial distance, but since we're kicking it from the ground, s=0.

Answer 7

So my maximum is 1? or .96?

Answer 8

Your t-value at the maximum is given by:
t = -b/2a from at^2 + bt + c
t = -31 / (2*-16) = 31/32
But we want the maximum height. We want to plug t=31/32 back into our H(t) equation to find the maximum height.

Answer 9

H(t) = -16t^2 + 31t + s
H(t) = -16(32/31)^2 + 31(32/31) + s

Answer 10

H(t) = -16(32/31)^2 + 31(32/31) + s
H(t) = -16(1.03) + 31(1.03)
H(t) = -16(32/31)^2 + 31(32/31)
H(t) = -16.48 + 31.93

Answer 11

s=0, because for your initial height you are kicking from the ground.
It is like, if you kicked 5 feet in the air with the same amount of force, it travels the same arc but it is 5 feet higher in general
.