How do you derive a Range prediction equation?

[genu]

Homework Statement

Derive the equations for v0 and R, and show how you made your prediction.

Homework Equations

d = v0t +1/2at^2

The Attempt at a Solution

The acceleration was zero, so I rewrote the equation:
R(range) = v0t

but then they substituted t with$$\sqrt{\frac{2Y}{g}}$$ to get

$$R=V{0}\sqrt{\frac{2Y}{g}$$

How did they get that for t?

also note: that Y is the vertical displacement of the ball to the floor.

let me know if I need to attach the diagram that they provided

 

[alphysicist]

Hi genu,

Homework Statement

Derive the equations for v0 and R, and show how you made your prediction.

Homework Equations

d = v0t +1/2at^2

The Attempt at a Solution

The acceleration was zero, so I rewrote the equation:
R(range) = v0t

but then they substituted t with$$\sqrt{\frac{2Y}{g}}$$ to get

$$R=V{0}\sqrt{\frac{2Y}{g}$$

How did they get that for t?

Think about what the range R means in this problem. In other words, as the object moves, the x-displacement keeps getting larger and larger until some event occurs; what event is that? The time when that occurs is what tells you how large your range is, and so the time when that occurs has to be used in your range equation. Does that help?