Momentum (Catching Ball on Ice)

[kevina]

The Question:

(1) You are standing on a sheet of ice that covers a parking lot; there is negligible friction between your feet and the ice. A friend throws you a 0.400 kg ball that is traveling horizontally at 10.2 m/s. Your mass is 73.4 kg.

(a) If you catch the ball, with what speed do you and the ball move afterward? Answer in cm/s.

(b) If the ball hits you and bounces off your chest, so that afterward it is moving horizontally at 8.70 m/s in the opposite direction, what is your speed after the collision? Answer in cm/s.

My Solution:
I was able to solve Part A. It's Part B I'm having trouble with. I used
(.400kg)(870cm/s)=(73.4kg)(v)
I solved for v and got 4.74cm/s, but the answer is wrong.
What am I doing wrong?

 

[Doc Al]

I used
(.400kg)(870cm/s)=(73.4kg)(v)

That would be true if the total momentum were zero, but it's not.

Set the initial momentum of the ball equal to the final momentum of the ball and you.
(Careful with signs: the ball bounces off and goes in the negative direction.)

 

[hagar852]

The Question:

(1) You are standing on a sheet of ice that covers a parking lot; there is negligible friction between your feet and the ice. A friend throws you a 0.400 kg ball that is traveling horizontally at 10.2 m/s. Your mass is 73.4 kg.

(a) If you catch the ball, with what speed do you and the ball move afterward? Answer in cm/s.

(b) If the ball hits you and bounces off your chest, so that afterward it is moving horizontally at 8.70 m/s in the opposite direction, what is your speed after the collision? Answer in cm/s.

My Solution:
I was able to solve Part A. It's Part B I'm having trouble with. I used
(.400kg)(870cm/s)=(73.4kg)(v)
I solved for v and got 4.74cm/s, but the answer is wrong.
What am I doing wrong?

Part B is an elastic collision.. and momentum is always conserved... the base eqaution is this... m1v1 (+/-) m2v2 = m1v3 (+/-) m2v4

v3 and v4 are the new velocities of the objects after the collision.

so it would be like this...

m1= ball
m2= you
v1=ball
v2= you
v3= ball after collision
v4= you after collision

m1v1 + 0 = -(m1v3) + (m2v4)

solving for v4 will equal

v4 = (m1v1) + (m1v3)
----------------
m2


=0.103m/s

=10.3 cm/s

 

[kevina]

Ahh.. I see.. I wasn't using the right equation. Thanks for the help Doc Al and hagar852. :)