Show that the centre of a rod of mass m and length l lies midway between the ends assuming that the rod has uniform cross section per unit length

Explanation:

The cross section per unit length is uniform, so ρ is constant.

The center of mass is therefore:

x_avg = (∫₀ᴸ x ρ dL) / (∫₀ᴸ ρ dL)

x_avg = (∫₀ᴸ x dL) / (∫₀ᴸ dL)

x_avg = (½ L²) / (L)

x_avg = ½ L

he kicked it 10 feet straight up into the air? i think this works.

seeing the graph would