:the launching velocity of a projectile is 20m/s at 53 degrees above the horizontal. what is the vertical component of its velocity at launch? neglecting air friction, which of these components remains constant throughout the flight path? which of these components determines the projectile's time in the air?

What is the vertical component of its velocity at launch? v0y = 20*sin(53) = 16 m/s 
Its horizontal component of velocity? v0x = 20*cos(53) = 12 m/s Neglect icing air friction, which of these components remains constant throughout the flight path? The horizontal component. (the vertical component is affected by gravity) 
Which of these components determines the projectile's time in the air? The vertical component. (because the projectile falls down after t = 2*v0*sin(53)/g, you can see it doesn't depend on the horizontal component)