Alumberjack (mass = 98 kg) is standing at rest on one end of a floating log (mass = 290 kg) that is also at rest. the lumberjack runs to the other end of the log, attaining a velocity of +3.3 m/s relative to the shore, and then hops onto an identical floating log that is initially at rest. neglect any friction and resistance between the logs and the water.
(a) what is the velocity of the first log just before the lumberjack jumps off? (indicate the direction of the velocity by the sign of your answers.)
m/s
(b) determine the velocity of the second log if the lumberjack comes to rest on it.
m/s

a)V= - 1.11 m/s  

b)V= 0.833 m/s

Explanation:

Given that

M (Mass of lumberjack)= 98 kg

Final velocity of lumberjack ,V₁= 3.3 m/s

m (Mass of log) = 290 kg

a)

There is no any external force that is why linear momentum will be conserved

Pi=Pf

initially both are at rest so Pi=0  ( P = m v)

Lets take speed of log is V

0= M V₁ + m V

V = - M V₁ / m

V= - 98  x  3.3 / 290

V= - 1.11 m/s  

b)

Now again from linear momentum conservation

(m + M )V =M V₁

V= M V₁(m+M)

By putting the values

V= 98  x 3.3/ (98 + 290 )

V= 0.833 m/s

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: