You are analyzing the possible defenses for an asteroid that is
going to crash into the earth.
Initially, the asteroid of mass ma is traveling
to the left with speed vai . A missile of mass
mm with initial speed vmi
to the right collides with the asteroid, and embedds itself inside
the asteroid. See the figure below.
Find the common final velocity of the missile and asteroid after
the collision.
Use an x-axis with positive pointing to the
right.
Solve algebraically first, then use the following values
for the parameters to get a value forvf
x :
ma = 5.2000E+9 kg
mm = 5.2000E+8 kg
vai x = -2100 m/s
vmi x = 3150 m/s
vf x = -1.62273×103 m/s
The missile then explodes, causing the asteroid to break into two chunks as indicated in the figure.
Solve algebraically for the final speeds of pieces 1 and
2 in terms of the masses (m1
andm2), the angles, the mass before the
explosion, and vf(the velocity after the
collision that you found above).
Then use the following values for the parameters to get values for
the speeds:
m1 = 2.2880E+9 kg
m2 = 3.4320E+9 kg
?1 = 39.3 degrees
?2 = 57.7 degrees
A) V1=?
B)V2=?
C)How much energy was released in the explosion?
*A) is not 6565.19 m/s
*B) is not 399.586 m/s
nitial momentum = final momentum
ma*vai x + mm*vmix = (ma+mm)*vfx
vfx = (-(5.2e9*2100)+(5.2e8*3150))/(5.2e9+5.2e8)
vfx = -1.62272x10^3 m/s
=================
2dimensional
initial momentum
P1x = -(ma+mm)*vfx = -3.525x10^6 kg m/s
P1y = 0
after collision
along y axis
v1y = v1*cos39.3 = 0.7738 *v1
v2y = v2*sin57.7 = -0.8453*v2
P2y = m1*v1y + m2*v2y
P2y = (2.288e9*0.7738*v1) -
(3.432e9*0.8453*v2)
P2y = 1.7705e9*v1 - 2.9011e9*v2
P1y = P2y
1.7705e9*v1 - 2.9011e9*v2=0
v1 = 1.63858v2 m/s
v1x = -v1*sin39.3 = -0.63*v1
v2x = -v2*cos57.7 = -0.5343*v2
along x axis
P2x = m1*v1x + m2*v2x
P2x = -(2.2880e9*v1*0.63) -
(3.4320e9*v2*0.5343)
P2x = -1.44144e9*v1 - 1.8337176e9*v2
P2x = P1x
-1.44144e9*v1 - 1.8337176e9*v2= -3.525x10^6 kg m/s
-3.393495e+9*1.63858v2 - 1.8337176e+9*v2= -3.525x10^6
v2 = 4.767x10^-4 m/s
v1 = 1.63858v2 = 7.811x10^-4 m/s
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