Double check this problem/solution I made?

[mrbutter]

I have to create my own physics question for homework which combines momentum/collisions with another unit (I chose forces/friction). Then I have to solve it.

Homework Statement

Lewis Hamilton is testing his new McLaren when suddenly he misses the pitlane break point and crashes into Kimi Raikkonen's Ferrari at 280 km/h. If Kimi was driving at 50km/h and the impact lasts for 0.3s and the coefficiant of friction is 0.3:
A) How far does each car slide?
B) Supposing that humans cannot survive over 80Gs, do either one of the drivers survive?

Homework Equations

impulse
p=p`
F=ma

The Attempt at a Solution

280km/h = 77.7 m/s
50kkm/h = 13.9 m/s
m1v1 + m2v2 = m1v1` + m2v2`
605(77.7) + 605(13.9) = 605(v1`) + 605(v2`)
V1` = 91.6 - V2`

v1 - v2 = v2` - v1`
77.7 - 13.9 = v2` - (91.6 - v2`)
V2` = 77.7 m/s
v1` = 13.9 m/s

//KIMI RAIKKONEN SLIDE
vf^2 - vi^2 = 2(a)(s)
a = -Ff / m
a = -ug
a = 0.3(9.8) = -2.94
0^2 - (77.7)^2 = 2(-2.94)(s)
s = 1026.75m

//LEWIS HAMILTON SLIDE
vf^2 - vi^2 = 2(a)(s)
a = -Ff / m
a = -ug
a = 0.3(9.8) = -2.94
0^2 - (13.9)^2 = 2(-2.94)(s)
s = 32.85m

//G FORCE FOR LEWIS HAMILTON
v1 = 605(77.7) = 47008.5
v1` = 605(13.9) = 8409.5
change in momentum = v1 - v1` = 38599
38599 = F * t
38599 = F * 0.3
F = 128663
G force = F / 9.8 = 13128.9

//G FORCE FOR KIMI RAIKKONEN
v1 = 605(13.9) = 8409.5
v1` = 605(77.7) = 47008.5

change in momentum = v1 - v1` = -38599
-38599 = F * t
-38599 = F * 0.3
F = -128663
G force = F / 9.8 = -13128.9





Okay! Now the thing is, those G forces looks REALLY high. I mean obviously the crash is going to produce a big number but I was guessing it would be between 75-200. Right now as you can see it's in the thousands.

Did I miss something?

P.S. I realize that this is obviously missing like a million real-world factors but it's for a high school physics class so no need to make it excessive with stuff we have not learned yet.

Thanks!

 

[jbsteele]

Yes, it looks like you missed something. It's important to remember that you need to factor in the mass of both cars when calculating the momentum and the force. The force experienced by each driver is the result of the combined momentum of the two cars, not just the momentum of one car. So you need to include both masses in your calculations. Additionally, you also need to account for the fact that the friction between the cars will reduce the force experienced by each driver. This means that the G forces experienced by each driver will be lower than the total G force calculated from the momentum of both cars.

 

[nlightner]

Your problem and solution seem to be well thought out and correct. However, it is always a good idea to double check your calculations and make sure you are using the correct equations and units. Additionally, it may be helpful to include some real-world factors such as the mass of the cars and the impact angle, as these can have an impact on the final results. Overall, your problem effectively combines momentum and forces/friction and your solution is comprehensive. Great job!