Answer:
a) -3.267 m/s
b) 2.227 m/s
Explanation:
As per the conservation of momentum
m1v1 + m2v2=0
m1= mass of log
m2 = mass of lumber jack
v1 = velocity of log
v2 = velocity of lumber jack
a) Velocity of first log
m/s
b) m1v1 + m2v2 = m3v3
Velocity of log
= 
Charge stored in a capacitor given by Q = C*V.
So, C = Q / V.
V=30V, Q=0.003C
C = 0.0001F or 100μF
Explanation:
Work done by winch = kinetic energy of car
∫ T ds = ½ mv²
∫ 225s ds = ½ mv²
225/2 s² = ½ mv²
225 s² = mv²
v = 15s / √m
Given s = 10 m and m = 2500 kg:
v = 15 (10) / √2500
v = 3 m/s
a. I've attached a plot of the surface. Each face is parameterized by
•
with
and
;
•
with
and
;
•
with
and
;
•
with
and
; and
•
with
and
.
b. Assuming you want outward flux, first compute the outward-facing normal vectors for each face.





Then integrate the dot product of <em>f</em> with each normal vector over the corresponding face.










c. You can get the total flux by summing all the fluxes found in part b; you end up with 42π - 56/3.
Alternatively, since <em>S</em> is closed, we can find the total flux by applying the divergence theorem.

where <em>R</em> is the interior of <em>S</em>. We have

The integral is easily computed in cylindrical coordinates:


as expected.