Suppose a particle is projected initially at speed $u$ downwards towards the ground at an angle $\alpha$ beneath the horizontal at a point $P$ above the ground. Let $O$ be a point on the ground, vertically below $P$. The particle will hits the ground at some point $R$.
If we throw the particle at the same speed $u$ towards the ground, but this time at a larger angle $\beta$, $\beta > \alpha$. The particle now hits the ground at some point $T$.
Is the horizontal distance $OT$ greater than or less than the horizontal distance $OR$?
I think the answer to this is that $OT < OR$.
However, this is from intuitive reasoning only: if the particle is thrown downwards at a larger angle, I feel like it is aimed more directly towards the ground and hence the distance $OT$ will be smaller than $OR$. It is hard to explain my intuition, but I'm pretty sure the distance is smaller.
Explaining this physically is difficult.
I tried to think that the range of a projectile equals $$u\cos \alpha \times t$$ where $t$ is the time of flight. If we increase $\alpha$ to $\beta$ (of course only up till $90^o$, which is the physical limit anyways), then this decreases for $t$ fixed. However, I don't think $t$ is fixed, so this is probably not the right explanation.
IS there any simple explanation for this problem? I feel like this is a 'simple' thought experiment and there is likely to be a simple qualitative explanation.