Suppose that a projectile is launched upward from the earth’s surface. Assume that the onl...

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

where υ = upward velocity (m/s), t = time (s), x = altitude (m) measured upward from the earth’s surface, g(0) = the gravitational acceleration at the earth’s surface  and R = the earth’s radius  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.