Question

Need help with formula: H(t) = -16^2 + vt + s

Jules kicks a soccer ball off the ground and into the air with an initial velocity of 25 feet per second. Assume the starting height of the ball is 0 feet. Approximately what maximum height does the soccer ball reach?

I know that v=25 and s=0
So now I have:
H(t) = -16^2 + 25t + s
But I have no idea how to find the maximum height.

(I've seen this question posted before and everyone said it needed more information, but this is all the question said)

Answer 1

The equation is h(t) = at^2 + vt + d where a = acceleration of gravity = - 32.174 ft/sec^2 v = 25 feet/sec d = starting height = 0 and h(t) = 0 when the ball hits the ground. So, 0 = - 32.174t^2 + 25t + 0 You can use the quadratic formula on that if you want, or you can solve like this: 0 = - 32.174t^2 + 25t 0 = t ( -32.174t + 25) So, one solution of that is t = 0, corresponding to the initial time when the ball is kicked. The other time is: 25 = 32.174t t = 25/32.174 = 0.777 seconds or approximately 0.8 seconds.