Ball bearing launched from point

[colerelm1]

Homework Statement

In my physics class we shot a ball bearing horizontally 85.4cm off the ground and we recorded the distance at which it landed. How can I find the initial velocity? The average distance traveled was 250.24 cm.

What if I was not provided I distance, how could I calculate the distance this ball would travel?

Homework Equations

I'm not sure.

The Attempt at a Solution

I have tried doing:

d sqrt(g / 2h)

2.5024(converted to m) sqrt( -9.8 / 2 x -85.4)
= 5.99 m/s

Is this right?

 

[Delphi51]

I don't recognize the formula d sqrt(g / 2h) but I get the same answer when I do it with good old horizontal (d=vt) and vertical (d = .5at²) parts.

 

[zgozvrm]

I don't recognize the formula d sqrt(g / 2h) but I get the same answer when I do it with good old horizontal (d=vt) and vertical (d = .5at²) parts.

They're the same:

(1) $$d = vt$$

(2) $$t = \frac{d}{v}$$


(3) $$h = \frac{a}{2}t^2$$

substitute t from equation (2) above:

(4) $$h = \frac{a}{2} \left(\frac{d}{v} \right)^2 = \frac{ad^2}{2v^2}$$

(5) $$v^2 = \frac{ad^2}{2h} = d^2 \left( \frac{a}{2h} \right)$$

(6) $$v = \sqrt{d^2 \left( \frac{a}{2h} \right)} = d \sqrt{\frac{a}{2h}}$$