If a stone is horizontally launched at a certain height, what will be the vertical velocity as it reaches the ground?

The vertical velocity of a stone launched horizontally as it reaches the ground can be calculated using the equation of motion:

v = u + gt

where:

• v is the final vertical velocity
• u is the initial vertical velocity
• g is the acceleration due to gravity
• t is the time it takes for the stone to hit the ground

Since the stone is launched horizontally, the initial vertical velocity (u) is 0. The acceleration due to gravity (g) is approximately 9.8 m/s². The time (t) it takes for the stone to hit the ground depends on the height from which it was launched.

To find t, we can use the equation:

h = ut + 0.5gt²

where h is the height. Since u is 0, the equation simplifies to:

h = 0.5gt²

Solving for t gives:

t = sqrt(2h/g)

Substituting this into the first equation gives:

v = g * sqrt(2h/g)

Simplifying this gives:

v = sqrt(2gh)

So the final vertical velocity of the stone as it hits the ground is the square root of twice the product of the acceleration due to gravity and the height from which it was launched.