A hockey puck B rests on a smooth surface of ice and is struck by a second puck

Question

A hockey puck B rests on a smooth surface of ice and is struck by a second puck A , which was originally traveling at v = 40.0m/s and which is deflected ?1 = 33.0? from its original direction. (See the figure below (Figure 1) .) Puck B acquires a velocity at a ?2 = 47.0? to the original direction of A . The pucks have the same mass.

Compute the speed of puck A after the collision.

Compute the speed of puck B after the collision.

What fraction of the original kinetic energy of puck A  dissipates during the collision?

A hockey puck B rests on a smooth surface of ice and is struck by a second puck A , which was originally traveling at v = 40.0m/s and which is deflected ?1 = 33.0? from its original direction. (See the figure below (Figure 1) .) Puck B acquires a velocity at a ?2 = 47.0? to the original direction of A . The pucks have the same mass. Compute the speed of puck A after the collision. Compute the speed of puck B after the collision. What fraction of the original kinetic energy of puck A dissipates during the collision?

Explanation / Answer

m1V1 + m2V2= m1U1 +m2U2 since V2=0
m1V1 = m1U1 +m2U2 now we have to decompose on components by assuming the puck A was moving in a positive x direction.

a)
For x components
m1V1cos(0) = m1U1cos(30) +m2U2cos(-45) since m1=m2 and cos(0)=1
V1 = U1cos(33) + U2cos(-47)

For y components
m1V1sin(0) = m1U1sin(33) +m2U2sin(-47)
or
m1U1sin(33) - m2U2sin(47) =0 since m1=m2
U1sin(33) - U2sin(47) =0

Two equation and two unknowns
since from the second equation
U1= U2 (sin(47) /sin(33)) substituting into the first we have
V1 = U2 (sin(47) /sin(33)) cos(33) + U2cos(-47)
U2= V1 /[(sin(47) /sin(33)) cos(33) + cos(-47)]
U2= 40 /[ 1.808]= 22.123 m/s

then
U1= U2 (sin(47) /sin(33)) =29.7072 m/s

b)
Kinetic energy before
Keb= 0.5m V1^2

Kinetic energy after
Kea= 0.5m (U1^2 +U2^2)

Fraction =Delta Ke/ Keb
Fraction Ke =0.5m(V1^2 - (U1^2 +U2^2))/0.5m(V1^2)

Fraction Ke =(V1^2 - (U1^2 +U2^2))/(V1^2)=

Fraction Ke =1- (U1^2 +U2^2))/(V1^2)

Fraction Ke =1- (29.7072 ^2 +22.123 ^2))/(40^2)
Fraction Ke = .1425

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