Projectile motion conceptual problem

[raymondlam]

Homework Statement

Two eggs, both housed in equivalent protective chambers, are pushed off a desk to the ground. One is pushed with greater force and travels further, while the other is pushed with less force and does not travel as far horizontally. Which egg is more likely to break? (Assuming the protective chamber perfectly snugly holds the egg so there is no jostling of the egg in the chamber)

Homework Equations

projectile motion, vertical and horizontal components

The Attempt at a Solution

In a situation where both eggs are pushed on a flat surface with no vertical drop, the horizontal force does not contribute to the egg breaking or not. It is the vertical force in the first situation that causes the egg to break. Therefore since the vertical force on both eggs in the first situation are the same, both eggs have the same likelihood of breaking (i.e. either both will break or neither will break) My father thinks otherwise, and that total component impact force is what matters, which is why I am posting this question.

 

[raymondlam]

Can someone let me know what is the right answer?

 

[rock.freak667]

Well instead of thinking about projectile motion, I'd think about impulse being the change in momentum Ft=mv-mu and t₂>t₁, compare Ft₁ to Ft₂.

 

[raymondlam]

I see, so

Egg 1
m =a
v1i> v2i
vf = 0
Ft1 = mvf - mv1i
Egg 2
m=a
v2i<v1i
v f = 0
Ft2 = mvf - mv2i

Since abs(Ft1)>abs(Ft2) impulse on the egg with more force horizontally is greater so it is more likely to break.