# Calculate Acceleration Given V0 and X

## Homework Statement

An astronaut kicks a football on a level area of planet Zog. He kicks the ball repeatedly at a wide range of angles from nearly zero to almost 90 deg above the horizontal, but always as hard as he can which gives an initial velocity of 11.7 m/s. The astronaut notices that the maximum distance the ball lands away from him is 90 m. Armed with this information and because he mastered Physics 2048, he returns to his landing craft and quickly calculates the acceleration of gravity g on planet Zog. What is that value?

V0 = 11.7 m/s
X = 90 m
X0 = 0 m
Y0 = 0 m

All of the relevant equations I think I can use involve time, which is not given. So, I do not know where to begin. If I can figure out where to start, I think I can figure it out pretty easily.

At what angle will the ball travel the maximum distance?

You have to go a little bit outside of plugging values into the kinematic equations.

Hint: The maximum distance the ball goes is 90m.

EDIT: Sid beat me to it.

Okay, that did get the ball rolling. I figured it was 45.0 degrees, so I calculated Vx and Vy.

Vx = 7.78 m/s
Vy = 7.78 m/s

Then I plugged in these values to this equation to find t:

X(t) = X0 + Vx0t
90 = 0 + 7.78t
11.6 s = t

So then I plug t = 11.6 s into this equation:

Y(t) = Y0 + Vy0t - 1/2(g)(t^2)
0 = 0 + 7.78(11.6) - 1/2(11.6^2)(g)
0 = 90.25 - 67.28g
67.28g = 90.25
g = 1.34 m/s^2

But, this is incorrect. :[

Are you sure you calculated the initial velocities correctly?

No I just realized that. For some reason I was putting 11 instead of 11.7 - silly me.

With new numbers, I got it right. Thanks guys!