To attain the maximum range a projectile has to be launched at 45 degrees if the landing spot and the launch spot are at the same height (neglecting air resistance effects.) Explain in a few sentences how the relation between the vertical and the horizontal components of the initial velocity affects the projectile range

see that the velocities are the components in a Cartesian system

Explanation:

The horizontal velocity of the projectile is the x-axis component of the initial velocity

          v₀ₓ = v₀ cos 45

vertical speed is

          = v₀ sin 45

therefore we see that the velocities are the components in a Cartesian system

r=rho l/a where a is the area, l is the length and rho is resistivity so the greater the area the lesser the resistance thats why the earth pin is thicker bcos current follow the shortest path, so less resistive .

3. dark matter

empty space could also be a simple vacuum