Displacement is the difference from the person's initial position and final position. In this problem, since the man is walking on orthogonal axes (x and y), we determine his displacement by using the pythagorean theorem. 

Distance travelled is the sum of all motion, which is:

The difference between distance and displacement is:

Measuring the total displacement means finding the norm of the vector that starts from the original spot to the final.

Since the object moved 2 feet east and 1 feet north , the norm of this vector can be found by doing:

For this question, we need to find out which graph represents constant velocity.

First, let's recall that velocity is defined as the amount of displacement that an object undergoes in a given amount of time. Hence, a graph in which the displacement is changing at a constant rate is showing a velocity that is constant. If this line is not straight in a graph of displacement vs. time, then the velocity is changing during the object's travel.

In a graph of acceleration vs. time, a straight flat line indicates that acceleration is not changing. And since acceleration is defined as a change in velocity with respect to time, a flat line indicates that the velocity is changing at a constant rate. Thus, in this scenario, velocity would not be constant (since it is changing at a constant rate). In an acceleration vs. time graph that contains an upward facing straight line, this indicates that the acceleration is increasing at a constant rate. And if acceleration is increasing at a constant rate, then the velocity would be increasing at an even greater rate (an exponential rate).

We will use Newton's 2nd law to solve this problem:

There are two forces acting on the sledder in the direction of their motion: friction and gravity. We are given the frictional force, so we just need to calculate the component of gravity in the direction of the sledder. We will start with the force of gravity:

And then to get the component in the direction of the sledder's motion, we will use the sin function:

If you're wondering why we use sine, think about the situation practically. As the angle grows, the hill gets steeper, and their will be more gravitational force in the direction of motion. Hence, we use sine. Now adding these forces together to get the net force:

We subtracted the friction force since it is always in the opposite direction of motion.

Now solving for acceleration:

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: