Question
Two asteroids
of equal mass collide as shown in the
figure. After the collision, asteroid A’s
trajectory is deflected by 30 degrees
from its initial motion. Asteroid B is
initially at rest and its final velocity
makes a 45 degree angle with respect
to the initial trajectory of asteroid A.
of equal mass collide as shown in the
figure. After the collision, asteroid A’s
trajectory is deflected by 30 degrees
from its initial motion. Asteroid B is
initially at rest and its final velocity
makes a 45 degree angle with respect
to the initial trajectory of asteroid A.
Answers
Damon
momentum x = m Via
momentum y = 0
after
m Via = m Va cos 30 + m Vb cos 45
0 = m Va sin 30 - m Vb sin 45
momentum y = 0
after
m Via = m Va cos 30 + m Vb cos 45
0 = m Va sin 30 - m Vb sin 45
GG
a) What is the final speed of each asteroid? Express your answer as a vector.
b) What fraction of asteroid A’s initial kinetic energy dissipates during the collision?
b) What fraction of asteroid A’s initial kinetic energy dissipates during the collision?
Damon
You have to use the two equations I derived to get Va and Vb in terms of Via, the initial speed of A
then you can do the x and y components
then you can do the x and y components
GG
The initial velocity before A hit B was 40 m/s
GG
I still don't understand what you are trying to say.
Damon
Vb = Va sin 30/sin 45
then
Via = Va cos 30 + (Va sin 30/sin 45)cos 45
then
Via = Va cos 30 + (Va sin 30/sin 45)cos 45
Damon
so Via = 40
You did not say that
use it
You did not say that
use it
Damon
so you can solve for Va, the speed of A after
then for Vb the speed of B after
then for Vb the speed of B after
GG
what is Va? That is what is confusing me the most
Damon
Va is the speed of A after collision
GG
how would i do part b?
Damon
once you have Va and Vb
Ke before = (1/2) m Via^2
Ke after = (1/2) m Va^2 + (1/2) m Vb^2
note m cancels everywhere in this problem
I think you can do the lost over the initial
Ke before = (1/2) m Via^2
Ke after = (1/2) m Va^2 + (1/2) m Vb^2
note m cancels everywhere in this problem
I think you can do the lost over the initial
David
Thank you so much
Damon
You are welcome.