You are analyzing the possible defenses for an asteroid that is going to crash i
ID: 1290112 • Letter: Y
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.
ma = 8.1000E+9 kg
mm = 4.0500E+8 kg
vai x = -2300 m/s
vmi x = 8740 m/s
1. vf x = ?
m1 = 5.9535E+9 kg
m2 = 2.5515E+9 kg
?1 = 34.7 degrees
?2 = 56.4 degrees
2. V1 = ?
3. V2 = ?
4. How much energy was released in the explosion?
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 Solve algebraically for the final speeds of pieces 1 and 2 in terms of the masses (m1 and m2), 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 = 5.9535E+9 kg m2 = 2.5515E+9 kg ?1 = 34.7 degrees ?2 = 56.4 degrees 2. V1 = ? 3. V2 = ? 4. How much energy was released in the explosion? ind 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 for vf x : ma = 8.1000E+9 kg mm = 4.0500E+8 kg vai x = -2300 m/s vmi x = 8740 m/s 1. vf x = ? The missile then explodes, causing the asteroid to break into two chunks as indicated in the figure.Explanation / Answer
initial momentum = final momentum
ma*vai x + mm*vmix = (ma+mm)*vfx
vfx = (-(8.1e9*2300)+(4.05e8*8740))/(8.1e9+4.05e8)
vfx = -1774.28 m/s
=================
2dimensional
initial momentum
P1x = -(ma+mm)*vfx = -1.50903e+13 kg m/s
P1y = 0
after collision
along y axis
v1y = v1*cos34.7 = 0.82214 *v1
v2y = v2*sin56.4 = -0.8329*v2
P2y = m1*v1y + m2*v2y
P2y = (5.9535e9*0.82214*v1) - (2.5515e9*0.8329*v2)
P2y = 4.89461049e+9*v1 - 2.122848e+9*v2
P1y = P2y
4.89461049e+9*v1 - 2.122848e+9*v2 = 0
v1 = 0.43371*v2 m/s
v1x = -v1*sin34.7 = -0.57*v1
v2x = -v2*cos56.4 = -0.5534
along x axis
P2x = m1*v1x + m2*v2x
P2x = -(5.9535e9*v1*0.57) - (2.5515e9*v2*0.5534)
P2x = -3.393495e+9*v1 - 1.4120001e+9*v2
P2x = P1x
-3.393495e+9*v1 - 1.4120001e+9*v2= -1.50903e+13
-3.393495e+9*0.43371*v2 - 1.4120001e+9*v2= -1.50903e+13
v2 = 5232.79 m/s
v1 = 0.43371*v2 = 0.43371*5232.7 = 2269.474317 m/s
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