I'm very confused over this question I had in my homework (someone told me you can't ask hw questions but I really want to know how to do this and I don't have access to a teacher right now) Sorry if this seems to easy. I'm not that good at math.
Suppose that an astronaut, wearing a space suit on Earth, can kick a ball a distance of 25 m. Using the datum gravitational acceleration is g=1.6 m/s^2, estimate how far he could kick the ball on the moon, using the same action and kicking at the same angle. (Remember significant figures and neglect air resistance. Assume that the launch and landing heights are the same. Do not use exponent notation.)
I think that you're supposed to use this equation maybe??: $$y=\left(\frac{v_{y0}}{v_{x0}}\right)x-\left(\frac{g}{2v_{x0}^2}\right)x^2$$ $v_{y0}$ I think is the starting velocity on the y-axis and $v_{x0}$ is the starting velocity on the x-axis. g is the gravity which is 9.8m/s^2(Earth) or 1.6m/s^2(Moon). y is the y-coordinate for the ball(which will be 0m cause the ball is touching the ground) and x is the x-coordinate for the ball (which will be 25m on the Earth).
First I wanted to find $v_{x0}$ and $v_{y0}$ so that I could find a velocity for both x and y that would work. So then I tried to use this equation by randomly choosing 10 for $v_{y0}$ so I could calculate $v_{x0}$. g was 9.8m/s^2 and x was 25m. I did this: $$0m=\left(\frac{10m/s}{v_{x0}}\right)25m-\left(\frac{9.8m/s^2}{2v_{x0}^2}\right)(25m)^2$$ And then I couldn't solve it.