Why a 30 mph vs. 40 mph Impact Makes a Difference

[Phykid]

Homework Statement

Our homework set today was to find out why is it that when you hit someone at 30mph they have a 20% chance of dying. Yet when you hit someone at 40mph they have a 90% chance of dying.

Homework Equations

KE = 1/2 M V^2

The Attempt at a Solution

First of all i found out that 1mile = 1.6km; which means 1 mile = 1600m
I then did 60x60 to find out the amount of seconds in 1 hour: which was 3600 seconds
I then divided 30 by 3600 to get the meters/second; which was 8.333 [reoccuring] m/s
Now I found out the Kinetic Energy. We were allowed to choose which car we used, and I used my fathers. This weighs 2090kg (Mazda 5)

KE = 2090 x (8.333^2) = 145127.278
145127.278 / 2 = 72563.63901 J

This is where the problem came

I then tried it with 40mph

40 / 3600 to get the m/s; which turned out as 0.0111 [reoccuring]
I now thought how the heck could that be right? But I continued & tried to do the equation.

Ke = 2090 x (0.011^2) = 0.25289
0.25289 / 2 = 0.126445

Okay now I'm very confused. Can anyone help me out?

When 30mph KE is 72563.63901 how is 40mph 0.0111?

Thanks,
Phykid

 

[Doc Al]

The calculation methods for 30 mph and 40 mph are identical, so recheck your arithmetic. Redo both conversions from mph to m/s.

First of all i found out that 1mile = 1.6km; which means 1 mile = 1600m
I then did 60x60 to find out the amount of seconds in 1 hour: which was 3600 seconds
I then divided 30 by 3600 to get the meters/second; which was 8.333 [reoccuring] m/s

You forgot the 1.6 factor in going from miles to km.

 

[Phykid]

I'm confused, sorry

EDIT: Ignore that, someone posted same time as me

 

[Doc Al]

Redo your conversion of 30 mph to m/s. Do it carefully, step by step.

 

[Phykid]

So how would I go about including the 1.6 into it?

Thanks,
Phykid

 

[Phykid]

So how would I go about including the 1.6 into it?

Thanks,
Phykid

Bump :O

 

[learningphysics]

Have a look at this link:

http://en.wikipedia.org/wiki/Units_conversion_by_factor-label

for conversions...

they have an example which is from miles/hr to m/s, just as you need.

 

[Phykid]

Brilliant!
Thanks for all your help

 

[Doc Al]

I hope you realize that in your first post you correctly described how 1 mile = 1.6 km = 1600 m (approx). But then for some reason you forgot to use that bit of info when you did your conversion from mph to m/s.

 

[Phykid]

I didnt until you pointed it out in your first post :)
thanks