You are analyzing the possible defenses for an asteroid that is going to crash i

Question

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

Explanation / Answer

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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