# Find the horizontal distance a ball will travel

1. May 27, 2006

### puddinandpie

Hi,
I have a physics question i'm not sure how to answer.
I need to find the horizontal distance a ball will travel when rolled down a ramp off a table.
The height of the table is 70.5cm
The time it took to leave the table and hit the ground is 0.335s
Using trial and error we found that the distance is around 69cm, but i need to prove this using a physics equation.
Anyone know how to do this?

2. May 27, 2006

### vsage

really you should recall that the ball will move horizontally at a constant speed for the amount of time it is in the air. From basic physics you should know how to calculate the time it takes for a ball to drop from a height d given its acceleration due to gravity.

3. May 28, 2006

### andrevdh

I assume that the end of the ramp was at the edge of the table launching the ball at an angle $\theta$ below the horizon (oops, you had to measure it!). This means that the x velocity will be
$$x=v_ot\cos(\theta)$$
and the y displacement (taken positive downwards)
$$y=v_ot\sin(\theta)+\frac{gt^2}{2}$$
Eliminate $v_o$ in the second equation using the first one.

4. May 29, 2006