Know your limits. If a problem is beyond control and cannot be changed at the moment, don't fight the situation
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In order to solve this problem, we will first need to find the electric field at the origin without the 3rd charge
E1 = (9x10^9)(13.4x10^-9)/(9.4x10^-2)^2 = 13648.7 V/m towards the negative y-axis
E2 = (9x10^9)(4.23x10^-9)/(4.99x10^-2)^2 = 15289.1 V/m towards the positive x-axis
The red arrow shows the direction of which the electric field points.
To make the electric field at the origin 0, we must find a location where q3 = the magnitude of q1 and q2
Etotal = sqrt(E1+E2) = 20494.97 V/m
E3 = 20494.97 = (9x10^9)(14.23x10^-9)/(d)^2
d = 0.079 m = 7.9 cm
The impulse J is equal to the magnitude of the force applied to the cannonball times the time it is applied:
But the impulse is also equal to the change in momentum of the cannonball:
If we put the two equations together, we find
And since we know the magnitude of the average force and the time, we can calculate the change in momentum:
But the impulse is also equal to the change in momentum of the cannonball:
If we put the two equations together, we find
And since we know the magnitude of the average force and the time, we can calculate the change in momentum: