What is the impulse on the ball from the string?

[Arman777]

Homework Statement

A ball of mass 1.00Kg is attached to a loose string fixed to a ceiling.The ball is released from the rest and falls 2.00m,where the string suddenly stops it.Find the impulse on it from the string.

Homework Equations

.[/B]
Kinematic equations
$\vec J=\vec FΔt=Δ\vec P$

The Attempt at a Solution

+z direction is upward.
$ΔH=v_0t+\frac 1 2at^2$ so this becames

$-2m=0-\frac 1 2gt^2$
$t=0.638 s$

and

$-2m=v_0t-\frac 1 2gt^2$
we know $t$ so
$-2-1.99=v_0(0.638s)$
$v_0=-6.25\frac m s$

then
$\vec J=\vec FΔt=Δ\vec P$
so
$P_f=m(-6.25)$
$P_i=m0$
$ΔP=-m6.25=-6.25Ns=J$

answer says $6.25Ns$ so there's no minus sign...
I didnt understand why...The question says "Find the impulse on it from the string" so the thing I found is some other impulse which created by something else..?

 

[jbriggs444]

The final momentum $P_f$ is what again? Did the problem statement not say that the string stops it?

 

[Arman777]

The final momentum $P_f$ is what again? Did the problem statement not say that the string stops it?

Is it wrong ?.I just wrote the velocity of the ball...Sure,spring stops it.I see I guess.

 

[jbriggs444]

Is it wrong ?.I just wrote the velocity of the ball...Sure,spring stops it.I see I guess.

What is the "initial" condition just before the string stops the ball?
What is the "final" condition just after the string stops the ball?

 

[Arman777]

Ohh $P_i$ is not $0$ its $-mv$ so $0-(-m v)=mv$ I solved

 

[Arman777]

Thank you