Question

Please refrane from answering if you are unfamiliar with MSExcel and inputing formulas for Cells. Thanks.

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Part b: Collision in Two-Dimensions

The law of conservation of momentum is true for any and everydirection. So, for an isolated system, the momentum in the x, y andz directions or any other direction does not change.

Consider two objects colliding in deep space. Since the two objectstogether can be considered an isolated system, the total momentumof the system (the sum of the momenta of the two objects) isconserved in both the x and y directions. That is

pi-x-total=pf-x-total or pix1+pix2=pfx1+pfx2

pi-y-total=pf-y-total or piy1+piy2=pfy1+pfy2

If we assume object one is moving in the x-direction, object two ismoving in the y-direction and the collision is perfectlyinelastic,
we can rewrite these equations as

m1*vix1=(m1+m2)vfx

m2*viy2=(m1+m2)vfy

These equations can be solved to find the x and y components of theobject's velocity after the collision. The magnitude of vf can befound using the Pythagorean Theorem. The direction of the objectsafter the collision can be found using the inverse cosinefunction

θ=cos-1(vfx/|vf|)

Since cos-1 outputs an angle between 0 and π radians, we must useθnew=2π-θold if vfy is negative to get a correct value. Use thebuilt in function 'if' to find the true value of θ. Afterwards,convert the angle into degrees using the built in function'degrees' .

i) Fill in the missing values in the table on the bottom usingformulas to find each value

This is the half of the tablethat is full so far

A = Mass1

B = Velocity initial 1

C = Mass2

D = Velocity intial 2

E = M2/M1

F = Vi2/Vi1

This is therest of the chart that needs formulas

G =Pi-x

H =Pi-y

I =|Pf|

J =Vf-x

K =Vf-y

L =|Vf|

M =θ

N = θ if Vi2< 0

O = θ(degrees)