I came out with 8 m/s for the final velocity Two asteroids collide as they trave

Question

I came out with 8 m/s for the final velocity

Two asteroids collide as they travel at right angles to each other. Asteroid A has mass 2000 kg and is traveling at 40 m/s to the right while asteroid B has mass of 8000kg and is traveling np at 7.5 m/s. If the asteroids stick together after the collision, what direction do they move in? What is the magnitude of the final velocity for each asteroid? How much kinetic energy is lost and what type of energy is it converted to? If the collision takes 2.0s, what is the average power generated during the collision?

Explanation / Answer

a)

x direction:

mA vA = (mA + mB) vx

==> vx = (mA vA)/(mA+mB) = (2000*40)/(2000+8000) = 8 m/s

y direction:

mB vB = (mA + mB) vy

==> vy = (mB vB)/(mA+mB) = (8000*7.50)/(2000+8000) = 6 m/s

theta = arctan(vy/vx) = arctan(6/8) = 36.9 degrees

b)

v = sqrt(6^2+8^2) = 10 m/s

c)

E = Ki - Kf

= (0.5 mA vA^2 + 0.5 mB vB^2) - 0.5 (mA+mB) v^2

= (0.5*2000*40*40+0.5*8000*7.5*7.5) - 0.5*(8000+2000)*10*10

= 1.3 x 10^6 J

It is converted to thermal energy.

d)

P = Q/t = 1.3e6/2 = 6.6 x 10^5 Watts

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