Answer:
Explanation:
For this problem, we just need to remember conservation of momentum, as there are no external forces in the horizontal direction:

where the suffix i means initial, and the suffix f means final.
The initial momentum will be:

as the second puck is initially at rest:

Using the unit vector
pointing in the original line of motion:



So:


Knowing the magnitude and directions relative to the x axis, we can find Cartesian representation of the vectors using the formula

So, our velocity vectors will be:


We got


So, we got the equations:

and
.
From the last one, we get:




and, for the first one:






so:

and


Explanation:
The solution is be found in the attachment.
Answer:
460.52 s
Explanation:
Since the instantaneous rate of change of the voltage is proportional to the voltage in the condenser, we have that
dV/dt ∝ V
dV/dt = kV
separating the variables, we have
dV/V = kdt
integrating both sides, we have
∫dV/V = ∫kdt
㏑(V/V₀) = kt
V/V₀ = 
Since the instantaneous rate of change of the voltage is -0.01 of the voltage dV/dt = -0.01V
Since dV/dt = kV
-0.01V = kV
k = -0.01
So, V/V₀ = 
V = V₀
Given that the voltage decreases by 90 %, we have that the remaining voltage (100 % - 90%)V₀ = 10%V₀ = 0.1V₀
So, V = 0.1V₀
Thus
V = V₀
0.1V₀ = V₀
0.1V₀/V₀ = 
0.1 = 
to find the time, t it takes the voltage to decrease by 90%, we taking natural logarithm of both sides, we have
㏑(0.01) = -0.01t
So, t = ㏑(0.01)/-0.01
t = -4.6052/-0.01
t = 460.52 s