A projectile is launched into the air on a parabolic trajectory. For t ≥ 0, its horizontal and vertical coordinates are x(t) = u0t and y(t) = −(1=2)gt2 + v0t, respectively, where u0 is the initial horizontal velocity, v0 is the initial vertical velocity, and g is the acceleration due to gravity. Recalling that u(t) = x′(t) and v(t) = y′(t) are the components of the velocity, the energy of the projectile is E(t) = 1 2 m(u2 + v2) + mgy