How Do You Calculate the Correct Drop Heights for Crash Helmet Testing?

[Mewhew]

First off, apologies if this is in the wrong section. It might be more of an engineering problem but I couldn't really work out exactly which section it should go in.
My young sister is doing an engineering course and has become stuck on a particular question, I offered to help not expecting it to confuse the hell out of me, however the question has definitely done so, possibly because it's been 10 years since I had to do any physics :) Any help on this would be appreciated.

Homework Statement

When testing a safety helmet it is dropped onto an anvil. The mass of the dummy head is 3.1kg. Two impact speeds are used; 5.42 ms-1 and 4.57 ms-1. The test requires that the deceleration experienced by the dummy head does not exceed 250 x g where g is the acceleration due to gravity.

a) Show that the heights from which the dummy and the helmet should be dropped in the test are the same as 1497 mm and 1064mm respectively. Show working and state assumptions.

b) Calculate maximum force experienced by 3.1kg head during acceptable impact.

Homework Equations

for a

time = $$\sqrt{2 * height/acceleration}$$

v = a*t

For b;

f=ma (?)

The Attempt at a Solution

The question asks me to prove that the heights given will result in the impact speeds given. Need to calculate the time so I can calculate the final speed. Time = sqrt of height * 2 / acceleration

t = $$\sqrt{2 * 1.497/9.8}$$

t = $$\sqrt{2.994/9.8}$$

t = $$\sqrt{0.305}$$

t = 0.552s

Substituting into the second formula gives;

v = a * t

v = 9.8 * 0.552

v = 5.41 ms

Which is close but not the value provided and I can't see where I'm going wrong.

For b I'm assuming I simply need to plug in the values to the formula f=ma.

Once again any help would be appreciated as this is making me feel very stupid.

 

[Carid]

Use 9.81 for g and round up the final answer.

 

[timmay]

A) Let's make the assumption that the potential energy of the falling headform is totally converted into kinetic energy at the point of impact. Finding expressions for gravitational potential energy and kinetic energy of a mass, setting them equal, simplifying and solving for height will get you where you're hoping to be.

B) You're correct - the maximum tolerable force is found that way. Don't forget that your value of acceleration is currently stated in g, whereas in SI units a Newton is equivalent to $$kgms^{-2}$$