Question

Please help! I know I am supposed to use the formula H(t) = -16t^2 + vt + s but unsure of actually solving it. Arianna kicks a soccer ball off the ground and into the air with an initial velocity of 42 feet per second. Assume the starting height of the ball is 0 feet. Approximately, how long does it take until the soccer ball hits the ground again?

Answer 1

H(t) = -16t^2 + vt + s

starting height of the ball is 0 feet means s is 0,
initial velocity of 42 feet per second means v= 42
so you have
H(t) = -16t^2 + 42t

H(t) is a parabola... the ball goes up and then it comes down
the first step to answering the question if find the t value of the vertex

can you do that ? one way is use -b/2a where a and b are the coefficients:
y= a t^2 +b t +c

Answer 2

after I used the t = -b/2a formula I got t = 1.3
afterwards I substitute it into the original equation?

Answer 3

you get t= 1.3125 (if we want to be accurate)

that is the time it takes to get to the top of the curve. The parabola is symmetric and it takes the same amount of time for the ball to come down.

Answer 4

I ended up getting (1.3, 27.56)... IS that correct? Does it take 1.3 seconds for the ball to get 27.56 feet?

Answer 5

Approximately, how long does it take until the soccer ball hits the ground again?

twice 1.3125

Answer 6

Unless there is more to the question, you don't need to figure out how high the ball goes..

Answer 7

no. That is all the question asks (: thank you so much!

Answer 8

So to hit the ground again it would be around 2.6 seconds?

Answer 9

you get t= 2.625 seconds

notice if you calculate the height at t= 2.625 you will get H= 0 (the ball is back on the ground!)

Answer 10

I get it! Thank you again!