First, we need to determine the rate at which the masses accelerate. We will start with Newton's 2nd law:

There are two forces acting on the system: gravity on each mass. For simplicity sake, we will examine these forces with respect to mass. Therefore, the force on mass B becomes an upward tension force on mass A. Now we need to clarify which direction is positive. For this problem, we'll say that a downward force is positive, and an upward force is negative.

We'll start with the gravitational force:

Now for tension. The tension force is simply the gravitational force applied to mass B:

Note that it's negative because it is in the upward direction

Now adding these together to get the net force:

Substituting this back into the original equation, we get:

Where m is the combination of both masses:

Rearrange for acceleration:

Now we can use a kinematics equation:

We are told that the system is initially at rest, so we can eliminate that term:

Rearranging for time, we get:

We know these values, so we can solve for time:

Now we can solve for final velocity using:

The arrow will have a vertical velocity of 0 when it reaches it's high point. Therefore, we can use the initial vertical velocity to calculate how long it takes to get there:

Then using the follow expression to determine time:

We can then multiply this time by the horizontal component of the arrow's velocity, which is constant since we are neglecting air resistance:

Plug this value into the distance formula to find the range.

To calculate the arrow's velocity relative to the ground, we will need to combine the velocity of the archer and the velocity of the arrow relative to the archer. To do this, we will first need to split the velocity of the arrow relative to the archer into it's vertical and horizontal components:

Then we can combine the two horizontal velocities (archer and arrow relative to archer). However, it should be noted that these two velocities are at right angles to each other (north and east), so we will need to use Pythagorean's theorem to combine them:

Now we can combine our total horizontal velocity with the vertical velocity to get our total velocity:

To find how fast the driver was going before applying the brakes, we use the following kinematics formula since acceleration is constant:

Where  is the displacement,  is the initial velocity (before applying the brakes),  is the final velocity (which is zero since the car came to a stop), and  is time. We can now plug in the known values into the above equation and solve for the initial velocity:

In order to know if the driver was speeding, we must convert this speed and/or the speed limit in the same units. Let's put this speed in kilometers per hour.

As we can see, the driver was exceeding the  speed limit and was thus speeding.

We need our kinematic equation that relates displacement, initial velocity, and acceleration:

We can neglect gravity in this problem since the statement says that the missile accelerates in a straight line at a constant rate.

Plugging in our values, we get:

The correct answer is .  Because we don't have time, we should use an equation that does not require a time variable, like 

where  is the final velocity,  is the initial velocity,  is the acceleration, and  is the distance traveled.  We are given , , and .  Therefore, we can put these values into our equation to solve for :

In order to find the acceleration, you must first take the derivative of the velocity:

The initial velocity does not affect the acceleration! It would only affect the position function! Afterwards, just plug in and solve for t:

The correct answer is , .  Average speed is:

, in 

We traveled a total of . Convert this to meters to get 

Then we must convert  to

Then divide to get your average speed. This gives us  

Velocity, on the other hand, is   in .  

Displacement is the the final distance from the initial position. Displacement is considered a state function. Only the final position matters; it doesn't matter how you get there. For example, if you start at point A and drive in a circle that covers , and end up at point A again, your displacement is . This is because your final position is the same as your initial position. So in this problem, because your final position is the same as your initial position, your displacement is .  

So for the average velocity.  

The correct answer is , 

Remember average speed is , also  

By converting  to  and  to , we get

This is also true for average velocity. Average velocity is  ,    

Displacement is the distance of the final position from the initial position. Because we do not change direction, the displacement is equal to the distance. That means that the average velocity will be equal to the average speed (time remains constant).