Suppose that a projectile is fired straight upward with initial velocity v₀ from the surface of the earth. If air resistance is not a factor, then its height x(t) at time t satisfies the initial value problem

Use the values g = 32.15 ft/s²  ≈ 0.006089 mi/s² for the gravitational acceleration of the earth at its surface and R = 3960 mi as the radius of the earth. If v₀ = 1 mi/s, find the maximum height attained by the projectile and its time of ascent to this height.

dx d12 8R (x + R)2' x (0) = 0, x'(0) = vo.