A ball is fired from ground level, with a fixed initial velocity, \(u\), at an angle \(\alpha\) to the ground. Assuming no one intercepts the ball, describe how the position at which it lands will vary with the angle of projection.

What might this relationship look like?

Can you sketch the path of the ball?

At what angle will the ball land furthest away?

How do you know this?

When will the ball land half as far away as this?

Consider the landing position above that is furthest away:

How much faster will the ball need to be fired so that it lands \(\quantity{1}{m}\) further away than this?

What about \(\quantity{2}{m}\) further away? What about \(d\) metres further away?