Physics Homework Help.?

Question

I will reward any good help with ten points.
This is part of my physics take home quiz. I worked them out but I just want confirmation to see if what I got is right.

A box rests on the (horizontal) back of a truck. The coefficient of Static friction b/w box and truck is 0.24. What maxmum distance can the truck travel (starting from rest and moving horizontally with constant acceleration) in 3.0 s without having the box slide?
I got 11 meters.

A 0.14 km wide river flows with uniform speed of 4 m/s toward east. It takes 20 s for a boat to cross to a point directly north of its starting point on the south bank. What is speed of boat relative to water? I got 8.1 m/s

Now, help me with thiz one. If the resultant force acting on a 2.0 kg is equal to (3i + 4j)N, what is the change in Kinectic energy as the object moves from (7i - 8j) m to (11i - 5j) m?
The answers are
a. 36 J b. 28J c. 32J d.24J 60J

Answer 1

a) Force on the box due to max acceleration witout moving the box = the maximum frictional force = 0.24* Normal force = 0.24*Weightof box = 0.24*mg

So max acceleration = 0.24*g = 2.352m/s^2
s = .5at^2 = 10.584

b)
this is a vector problem
the boat needs to be driven towards west inorder to cross exactly to a point at north.
resultant speed of boat = 140/20 = 7m/s
so using pythagorian theorem, U^2 = 7^2 +4^2, or U=sqrt(65) = 8.0623

c)displacement = (11i - 5j) - (7i - 8j) = (4i + 3j)
force = (3i + 4j)
work done = Fs = (3i + 4j)(4i + 3j) = 12 + 12=24

So change in Kinectic energy = work done = 24J

Answer 2

change in kinetic energy is nothing but work done
work done is nothing but force*distance travelled
distance travelled is 11i-5j-(7i-8j) = 4i+3j
force is 3i+4j
change in kinetic energy is 3i+4j*4i+3j=24j

Answer 3

1.) normal force

2.) Vectors

3.) Vector sums and energy conservation