← Projectiles: two independent motions

Horizontal launch means zero initial vertical velocity

A marble rolls toward the edge of a level table. While it rolls, its velocity points parallel to the tabletop: fully sideways, none of it up or down. Then it reaches the edge.

A projectile's launch velocity is its velocity at the instant it leaves the surface or the hand. For the marble, that is the instant it leaves the edge.

At the edge, the marble still moves parallel to the tabletop. Its launch velocity is entirely sideways.

tabletoplaunch velocity: entirely horizontal (v_y = 0)
At the instant it leaves the edge, the velocity points parallel to the tabletop: the vertical component is zero.

Split the launch velocity into components. The horizontal component is all of it. The vertical component is zero.

tabletophorizontal component: the full launch valuevertical component: v_y = 0 (a dot, no arrow)
Split the launch velocity: the horizontal component is all of it; the vertical component is zero.
So the marble leaves the edge with v_y = 0. A horizontally launched projectile starts with zero vertical velocity, since its launch velocity points entirely sideways.

Why does a ball rolling off a level shelf start its flight with zero vertical velocity?

Zero is only the starting value. Free fall begins at the edge, and the vertical velocity grows downward from the first instant of flight.

tabletophorizontal component: unchangedvertical component: growing downward
A moment later: zero was only the starting value. Free fall has begun, and the vertical velocity grows downward.

The horizontal component keeps its full launch value through the flight, as always.

A book slides off a level desk at 1.2 m/s. State the horizontal and vertical components of its velocity at the instant it leaves the desk.

The book leaves the desk moving parallel to the desktop.

So its launch velocity is entirely horizontal.

horizontal component = 1.2 m/s

vertical component = 0 m/s

Horizontal: 1.2 m/s. Vertical: 0 m/s.

Paulo says a marble leaving a level tabletop horizontally at 3 m/s has no vertical velocity at that instant. Is he correct?

A coin leaves a level shelf moving horizontally. Is its vertical velocity still zero 0.2 s into the flight?

Your turn

Which launch starts a projectile with zero vertical velocity?

A toy truck rolls off the edge of a level porch. Why is its vertical velocity zero at the instant it leaves?

A marble leaves a level counter moving horizontally at 1.5 m/s. Enter its vertical velocity, in m/s, at that instant.