Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collid

Question

Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collide with a glancing blow. Asteroid A, which was initially traveling at vA1 = 40.0 m/s with respect to an inertial frame in which asteroid B was at rest, is deflected 30.0 ? from its original direction, while asteroid B travels at 45.0 ? to the original direction of A, as shown in (Figure 1) .

Part A

Find the speed of asteroid A after the collision.

vA2 =

Part B

Find the speed of asteroid B after the collision

vB2 =

Part C

What fraction of the original kinetic energy of asteroid A dissipates during this collision?

Thank you I do not know how to solve this!

Explanation / Answer

using law of conservation of momentum

(mA*uA)+(0) = mA*VA*cos(30) + mB*VB*cos(45)

given that mA = mB

then uA = VA*cos(30) + VB*cos(45) = 40

and also

VA*sin(30) = VB*sin(45)

VA/VB = sin(45)/sin(30) = 1.414

VA = 1.414*VB

UA = (1.414*VB*cos(30)) + (VB*cos(45)) = 40

VB = 20.7 m/s = vB2

VA = 1.414*20.7 = 29.3 m/s = vA2

C) change in KE = Kf-Ki = ((0.5*mA*vA)^2 - (0.5*mA*uA^2))/(0.5*mA*uA^2)

kf-ki = (29.3^2-40^2)/40^2 = -0.463 J

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects