# Impulses, impulses everywhere...

**Classical Mechanics**Level 5

It is rotating at an angular velocity of \(w\sqrt { 2 } \) in a plane making 45 degrees with the plane in which it was translating initially.

The wall is at a distance \(D\) from the launch point,

such that

1) \({ 2u }^{ 2 }H<{ D }^{ 2 }g\)

2) \(D\quad <\quad u\sqrt { \frac { 2H }{ g } } +\frac { sin(2\quad arctan(\sqrt { \frac { gH }{ 2 } } ) }{ g }\)

Let the friction on the floor be sufficiently high to just stop rotation (**See Note**)

Find the average force it exerts on the wall when it collides with the wall provided the impact lasts for 2 seconds and it is perfectly elastic

if the answer is 'a'

input the **square of a** to the **closest integer** (if it is not an integer)

**DETAILS AND ASSUMPTIONS**

1) u (initial velocity)=0.7320 approximate as (root(3)-1)

2)w (initial angular velocity)=2.5

4)Mass of Ball=1

5)Radius of ball =1

**All in S.I unit**

**NOTE**

1) the inequalities are not the exact necessary conditions example,, if the question requires a<b then i may have altered it as a<b-1 because the second inequality naturally implies the first one,, so as to not reveal the answer,

2) also the figure shows a satelite view of the problem

3) Considering the balls rotation as a vector superposition of angular velocities along different axes might help

This problem was inspired by Let's play cricket