Question

A soccer ball is kicked from the ground into the air. When the ball is at a height of 8.55 m, its velocity is (vx,vy) = (4.91,3.97) m/s.
I am looking for the maximum height and the horizontal distance the ball traveled

I'm not asking for answers, but how to do them. For example, just the steps

Answer 1

well you have the x and y

Answer 2

so take your y and solve velocity initial with the equation\[v _{y}^{2}=v _{0y}^{2}-2g \Delta y\] and your delta y is 8.55m

Answer 3

so I got an initial y of about 13.7 m/s with g as 10 not 9.8

Answer 4

so take that and plug it into
\[v _{y}=v _{0y}-g t\]
if you set vy as 0 you will get the time to your max height

Answer 5

and then when you have the time of your max height you need to plug it into\[\Delta y=1/2(v_{y}+v _{0y})t\]
to get the highest point

Answer 6

and then if you take the time to your max height multiply it y 2 you will get when the ball hits the ground since trise=tfall

Answer 7

and so plug the time until the ball hits the ground into the equation for finding delta x
\[\Delta x=v _{0x}t-1/2at ^{2} \] since your acceleration is zero you are left with
\[\Delta x=v _{0x}t\]

Answer 8

hope that helps