In: Physics
with a velocity v = 4.6i m/s. It the strikes the six ball, which has an identical mass and is initially at rest. After the collision the eight ball is deflected by an angle of θ = 26° and the six ball is deflected by an angle of Φ = 35°, as shown in the figure.
Part (a) Write an expression for the magnitude of six ball's velocity, in terms of the angles given in the problem and the magnitude of the eight ball's initial velocity, v.
Part (b) What is the magnitude of the velocity, in meters per second, of the six ball?
Part (c) What is the magnitude of the velocity of the eight ball, in meters per second, after the collision?
m1 = m = 0.5
kg
m2 = m = 0.5 kg
befor collision
v1 =
4.6i
v2 = 0
after collision
v1'x = v1'*cos26 v2'x = v2'*cos35
v1'y =
v1'*sin26
v2'y = v2'*sin35
from momentum conservation
along y
Piy = Pfy
0 = m1*v1'y + m2*v2'y
v1'y = v2'y
v1'*sin26 = v2'*sin35
v1' = v2'*sin35/sin26......(1)
along x axis
Pix = Pfx
m1*v = m1*v1'x + m2*v2'x
v = v1'*cos26 + v2'*cos35.......(2)
using 1 in 2
v = v2'*sin35*cos26/sin26 + v2'*cos35
v*sin26 = v2'*sin35*cos26 + v2' *cos35*sin26
v*sin26 = v2'*sin(35+26)
v*sin26 = v2'*sin61 <------answer
-------
part(b)
v2' = 4.6*sin26/sin61 = 2.3 m/s
<------answer
part(c)
v1' = v2'*sin35/sin26
v1' = 3 m/s <<------answer