Suppose that a projectile is fired straight upward from the surface of the earth with init...

Suppose that a projectile is fired straight upward from the surface of the earth with initial velocity v0 < . Then its height y(t) above the surface satisfies the initial value problem

Substitute dv/dt − v(dv/dy) and then integrate to obtain

for the velocity v of the projectile at height y. What maximum altitude does it reach if its initial velocity is 1 km/s?