Respuesta :
Answer:
-13.5 m/s^2
-1.35m/s
Explanation
First, find the momentum of the paintball by using the formula [tex]p=mv[/tex].
[tex]p=0.15*45[/tex]
[tex]p = 6.75[/tex]
The next step would be to find the change of momentum of the gun. Since the gun was at rest it had a momentum of 0. Momentum acts in different directions equally, therefore we can set up the equation for the acceleration:
FΔt=Δp
Where F is force, Δt is the change of time and Δp is the change of momentum.
Since we solve for acceleration, we can convert F to ma to get:
maΔt=Δp
Substitute values:
5a*(0.1-0)=-6.75
5a=-67.5
a=-13.5
Our a is -13.5m/s^2, it's negative since the direction it's acting on is opposite of the paintball.
Now we can find velocity (and double-check our work!).
The first way to solve for velocity is:
[tex]V=Vi+at[/tex]
Where V is final velocity, Vi is initial, a is acceleration and t is time.
substitute values:
[tex]V=0-13.5*0.1\\V=-1.35m/s[/tex]
If we are correct, using the formula p=mv, we should get the same result (remember, our momentum is negative).
[tex]p=mv\\-6.75=5v\\-1.35m/s=v[/tex]
Hope this helps!
