Question

At a certain point along the path in projectile motion, the projectile has a velocity v whose scalar components are vx = +30 m/s and vy = +40 m/s. As the projectile moves along the path, what would be its minimum speed?

Answer 1

The speed of the projectile would be the magnitude of its horizontal and vertical components combined. Therefore, the minimum speed during its flight will be when it has reached its highest point and the vertical component is 0
At that instant, the speed is:
s = √(30² + 0²)
s = 30 m/s

Answer 2

At the maximum point on the projectile motion path, the object start moving downward due to gravity. Thus at the maximum point, the vertical component of its velocity is zero. Hence only horizontal component of the velocity of project exist. 
So the minimum speed of the project will be 30m/s.