So I am having a issue with this problem and cant see a way of solving it.
The world discus champion is temporarily living on a planet which has half the radius of the Earth. He discovers that he can throw the discus 10 times further than he can on Earth. Estimate the relative density of this planet compared to that of Earth. Ignore any effect of air resistance.
My initial assumption is that the discus is thrown in the air vertically and I could calculate the K.E of throwing up in the air.
So kinetic energy from earth
$v^2=u^2-2gy$
$u=\sqrt{2gy}$
$K.E=\frac{1}{2}m_\text{disc}2gy=m_\text{disc}gy$
but here my issue I was thinking of using gravitational potential to setup the following equation.
$gy=\frac{-GM_{p}}{r_{E}+y}$
but that my issue, because of the negative it make no sense to me how you can approach this question another way, to form a numerical solution.
Have I overlooked something?
They are probably ignoring the fact that the discus gets lift from the air and considering it a projectile. They then talk about distance thrown, which is maximized when the launch angle is $45^\circ$. You should determine by what factor the acceleration of gravity has to change to make the distance covered increase by a factor $10$. Lowering $g$ will let the discus stay in the air longer, so it will cover more ground.
Then note that the surface gravity of a planet scales as the product of the radius and the density. You are told that the radius is cut in half, so you need to get the rest of the factor out of the density.