# Velocity when hitting wall

1. Mar 2, 2012

### DarkFalz

Hello,

i have the following questions. Lets assume that i throw a ball with mass 1kg and velocity 10 m/s at a wall with mass 100000000000000000 and velocity 0

using linear momentum i have in the beginning i have p = 1*10+ 100000000000000*0 = 10

after the impact the wall stays still and so the ball should go back with the same speed but the opposite direction, so i should have

Vf = - Vi

but if i do the calculations:

10 = 1*vf + 100000000000000*0 <=> 10 = vf <=> vf = 10

what have i done wrong? the speed should be -10

2. Mar 2, 2012

### Hassan2

The velocity of the wall after collision is not exactly zero. Even with a small velocity, the product of the mass and the velocity is not negligible.

You should solve it this way:

m: mass of the ball
M: mass of the wall
v0: the velocity of the ball before collision
v: the velocity of the ball after collision
V: the velocity of the wall after collision

$mv_{0}=mv+MV$

This equation is true for both elastic and inelastic collisions but it has two unknowns. We need another equation to find the velocities. That is the conservation of energy. For an elastic collision, the kinetic energy is conserved:

$\frac{1}{2}$mv$_{0}^{2}$=$\frac{1}{2}$mv$^{2}$+$\frac{1}{2}$MV$^{2}$

from the two equations, you obtain

v=$\frac{m-M}{m+M}v_{0}$

and

V=$\frac{2m}{m+M}v_{0}$

Last edited: Mar 3, 2012
3. Mar 2, 2012

### apb000

You need to clarify the question, in particular the line after "but if i do the calculations:" is not clear. Try writing the equation you're using in its general form (using letters) then in the line directly under it, repeat the equation with the specific numbers filled in, and use units.

It looks like what you're trying to say is,
initial momentum of the ball = negative the final momentum of the ball (the wall is irrelevant since it's always multiplied by zero)
pf=-pi
mfvf=-mivi
1 kg x vf=-1 kg x 10 m/s
So vf=-10 m/s.
Now, what's the question?