# Homework Help: How fast was he moving when he hit the parked car?

1. Jul 4, 2010

### Derekj032

First off, I'm new to this forum so I would like to say hello to everyone on here.

Secondly, I'm helping fellow law school friends out with a mock trial this coming week and was in need of some help. The fake trial is about a young man who hit a car on his motorcycle etc... lawsuit...etc..

I have determined that the young man weighed 210pds and was traveling on a 400pd motorcycle. He hit a stationary car and traveled 20 feet from the point of impact. How fast was he moving when he hit the parked car? I don't even know if there is a way to answer this, as I'm terrible with math. Rest assured, this is not a homework question or anything like that. I'm just trying to determine his rate of speed for the fake trial. I thought that this was a good thing to determine, as I imagine most people will not be inclined to use mathematical calculations in this case.

If someone can answer this question and post the formula I would be thrilled. Thanks in advance.

2. Jul 4, 2010

### mgb_phys

In theory yes, if you know either
1, the height above the ground he left the bike and the drag coefficent of a head-on biker you can calculate how long he flew for (it's the basic cannon ball equation)
or
2, The coefficent of sliding friction if you assume he slid along the ground.

In practice you are going to be inaccurate, it's very sensitive to things like exactly how you land and which bits of clothing stick to the ground.

3. Jul 4, 2010

### Derekj032

The height would be 30.5 inches from the ground to the top of the seat. I really know next to nothing about math, hence why i chose law school... lol

4. Jul 4, 2010

### Derekj032

I'm only looking for an approximation of the possible speed. In the case the guy claims he was traveling around 25mph, which was the posted limit. A few witnesses claim he was traveling in excess of 50-55mph. I just want to know if either of the aforementioned claims can be looked at as incorrect.

5. Jul 4, 2010

### mgb_phys

Neglecting air resistance if you fire an object horizontally 30.5" inches above the ground and they hit the ground after travelling 20ft then:

Time to fall (switching to metric)
s = ut + 1/2at^2 , u=0, a=g=9.8m/s^2
0.77m = 1/2 * 9.8m/s^2 * t^2
t = sqrt ( 0.77 / 2*9.8) = 0.2secs

To travel 20" in 0.2 secs you have to be going at 20"/0.2secs = 100ft/s = 68mph

in practice they would travel less far at this speed (because of air resistance) so they would have to be going faster than this