Hi there!
We can use the work-energy theorem to solve.
Recall that:

The initial kinetic energy is 0 J because the crate begins from rest, so we can plug in the given values for mass and final velocity:

Now, we can define work:

Now, plug in the values:

Solve for theta:

Answer:
a) 1111.0 seconds
b) 833.3 s
c) Because of proportions
Explanation:
a) Total time of round trip is the sum of time upriver and time downriver

Time upriver is calculated with the net speed of student and 0.500 km:

(Becareful with units 0.5 km= 500m) Similarly of downriver:

So the sum is:

b) Still water does not affect student speed, so total time would be simply:

c) For the upriver trip, student moved half the distance in half speed of the calculation in b), so it kept the same ratio and therefore, same time. So the aditional time is actually the downriver.
Answer:
1) Mass that needs to be converted at 100% efficiency is 0.3504 kg
2) Mass that needs to be converted at 30% efficiency is 1.168 kg
Explanation:
By the principle of mass energy equivalence we have

where,
'E' is the energy produced
'm' is the mass consumed
'c' is the velocity of light in free space
Now the energy produced by the reactor in 1 year equals

Thus the mass that is covertred at 100% efficiency is

Part 2)
At 30% efficiency the mass converted equals

Answer:
tbh vector does not have any direction at all the answer is 0