why is it when a projectile is fired that it has a maximum range when the launch angle is 90 degrees. would it not just fire up vertically and fall back down with no range at all.
why is it when a projectile is fired that it has a maximum range when the launch angle is 90 degrees. would it not just fire up vertically and fall back down with no range at all.
You are right. Maximum range is achieved at a launch angle of 45 degrees (for the case where y0 and yf are the same.)
why is it when a projectile is fired that it has a maximum range when the launch angle is 90 degrees. would it not just fire up vertically and fall back down with no range at all.
??? ... max range is achieved if the launch angle is 45 degrees if $\Delta y = 0$
If $\Delta y = 0$, then $\Delta x = \dfrac{v_0^2 \sin(2\theta)}{g}$ is a maximum when $\sin(2\theta) = 1 \implies \theta = 45^\circ$