Suppose that a projectile is launched upward from the earth’s surface. Assume that the only force acting on the object is the downward force of gravity. Under these conditions, a force balance can be used to derive,

dυ/dt = -g(0) R²/(R + x)²

where υ = upward velocity (m/s), t = time (s), x = altitude (m) measured upwards from the earth’s surface, g(0) = the gravitational acceleration at the earth’s surface (= 9.81 m/s²), and R = the earth’s radius (= 6.37 x 10⁶ m). Recognizing that dx/dt = υ, use Euler’s method to determine the maximum height that would be obtained if υ(t = 0) = 1400 m/s.