In this question, we are given a lot of information.
It is important that we acknowledge what the question is actually asking.
We are asked for the average speed between X and Y.
With this in mind, we can use:

v = 0.4ms^-1

You should know that the horizontal speed of the stone does not change; it is equal to the inital speed of 20ms^-1.

To work out the vertical speed of the stone, we need to list our data:

initial vertical speed(u) = 0ms^-1
acceleration(a) = 9.8ms^-2
final vertical speed(v) = ?

Now, we can use:

v = at

v = 9.8 x 3

v = 29.4ms^-1

So
horizonal speed = 20ms^-1
vertical speed = 29.4ms^-1

First, lets identify the formula we need to use.
We are asked for the change in gravitational potential energy, which is effectively how much energy is lost.
So we can use:

Ep = mgh

Notice how we don't actually have the mass of the child, so we need to work this out using:

w = mg

Now we sub in our values and re-arrange:

250 = m x 9.8

m = 25.5kg

Now we can calculate the change in gravitational potential energy:

Note that the height whenever dealing with gravitational potential energy is the vertical height:

Ep = 25.5 x 9.8 x 2

Ep = 499.8

Ep = 500J

First, lets calculate the unbalanced force acting on the box:

Unbalanced Force(F_UN) = Total Force - Frictional Force

F_UN = 20 - 4

F_UN = 16N

Now that we have the unbalanced force(F_UN) and the acceleration(a), we can use and re-arrange:

F_UN = ma

16 = m x 1.6

m = 10kg

(a) A simple question, using:

w = mg

w = 50 000 x 9.8

w = 490 000N

(b) The trick to this question is in the wording, where it says "State".
This usually means no calculations need to be done.
Since the plane is flying horizontally at a constant height:

Upward Force = 490 000N

(c) We always need a diagram for calculating resultant force.
Remember to draw vectors tip to tail:

Where "F" is the magnitude of the resultant force, and "x" is the direction of the resultant force.

Now we use pythagoras to calculate the magnitude of the resultant force:

F ² = (3.2 x 10⁴)² + (4.4 x 10⁴)²

F = 5.4 x 10⁴N

Now we calculate the direction of the resultant force:

x = 54°

We need the direction as a bearing, so we draw a North line on our diagram.
Then we subtract the angle we just calculated from 90 to get the bearing:

So the bearing is 036(Remember bearings are displayed with only three figures)

Finally, we need to state the resultant force:

Resultant Force = 5.4 x 10⁴N at a bearing of 036

(a) To get the acceleration, we use:

Where v is the final vertical speed, u is the inital vertical velocity and t is the time.
Subbing in our values:

a = 0.1ms^-2

(b) To get the distance travelled, we need to calculate the area under the graph.
We need to split the graph into two separate areas:

d = area under speed time graph:

d = (0.5 x 60 x 6) + (40 x 6)

d = 420m

(c) Simply just use the speed formula:

v = 4.2ms^-1

(d) Simply just use the weight formula:

w = mg

w = 400 x 9.8

w = 3920N

(e) The best way to go about this question is to draw a freebody diagram to get a sense of what is actually happening:

For the balloon to accelerate upwards, the total upward force must be greater than the size of the weight of the balloon.
This means that there will be an unbalanced force acting upwards, causing an the balloon to accelerate upwards.

To calculate the size of the unbalanced force, we use:

F_UN = ma

F_UN = 400 x 0.1

F_UN = 40N

Now, we add the unbalanced force to the weight to get the total upward force.

Total upward force = F_UN + Weight

Total upward force = 40 + 3920

Total upward force = 3960N