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It depends on the angle and speed at which it is fired.

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Q: What is the vertical velocity of a projectile at the lowest point in trajectory?
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What is the value of the vertical speed at the highest point of the projectile's trajectory?

The value of the vertical speed at the highest point of the projectile's trajectory is the lowest speed at the maximum height reached.


With out air pressure at what point or points in its path does a projectile have its minimum speed and its maximum?

Without air friction, the horizontal component of the velocity will be constant. The vertical component of the velocity will be a maximum at the lowest point in its motion and at a minimum at the highest point in its motion. Therefore the minimum is at the highest point in its motion- Potential energy max Kinetic Energy min and the maximum is at its lowest point in the motion- KE is max PE min


Which is the total velocity of a projectile at maximum height?

It depends. If the projectile goes straight up and straight down, its velocity will be zero at the top. If the projectile is a baseball about halfway between the pitcher and the bat, its velocity might be 150 km/h.


A projectile fired from the ground follows a parabolic path The speed of the projectile is minimum at the top of its path?

Yep that is correct. To understand this it may help you to draw a parabola. If you draw a line from the top of the parabola back to the ground you'd notice either side of this line is symmetrical. This isn't quite what happens to a projectile (following a parabolic path), but because of the nature of the question, effects such as air resistance can be ignored. As the projectile approaches the top of its path, the vertical component of its velocity approaches zero. As the projectile begins to fall the magnitude of the vertical component of the projectile begins to increase. The only force that acts on the projectile during flight is gravity which pulls it towards the earth. Since this force and the horizontal component of the projectiles velocity are at right angles to each other, the horizontal component of the velocity is unaffected during flight . This explains the symmetry of the parabola and also means the time to reach the top of path equals the time from the top of path back to the ground. The projectile will hit the ground with the same speed as it left the ground. If you draw a horizontal line through the parabola, at the two points where the line and the parabola cross, the speed of the projectile will be the same. The only change to the balls speed during the flight comes as the vertical component of its velocity tends to zero as it reaches the top of the curve and then falling back down due to gravity. I'm unsure of your physics knowledge but hopefully this doesn't confuse you. If you have learned about vectors, then this can be simply understood/explained.


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What is the vertical distance from the crest of a wave to the trough?

Vertical distance from a wave's highest point to it's lowest point is called the amplitude of a wave.