Science Buddies: "Ask an Expert"

Hi,

I was doing the Gauss Rifle project on science buddies and I come across an equation i.e

Velocity (m/s) = Horizontal distance between the table and the ball (m) X Square root of
(gravitational acceleration (m/s2) divided by [2 X height of the table (m)])

Can someone please help me figure out HOW was it derived and WHY will it work?
Because I think one has to use projectile motion and stuff to figure out the velocity.

Here's the link if you need to see it yourself.

https://www.sciencebuddies.org/science- ... #procedure

Hi Aryie,

The equation provided is projectile motion, but with a few assumptions made so that the formula is applicable to this scenario. The horizontal component has no acceleration since the ball is no longer accelerating when it leaves the table. Due to the ball moving in a perfectly horizontal direction, the ball does not have a vertical velocity. However, gravity will be accelerating the ball downward.

This equation is for velocity, which is a vector. This is a 2-dimensional equation so we will have a horizontal component and a vertical component. We can use equations of motion to derive the velocity. Due to this being a 2-dimensional problem, we will need two equations to derive the velocity. I will provide you a few equations to get you moving in the right direction.

Horizontal:
Displacement (x) can be written as a function of Velocity (v) and Time (t)
x = vt

Vertical
Height (h) can be written as the distance travelled with no initial velocity but with an acceleration
h = 1/2 g t^2

Start by recognizing that time is a component of both equations. I will check back if you need additional assistance.

-AeroSE