The ideas we are practicing in these exercises can be put to practical use. My son likes to shoot arrows. He was wondering at what speed the arrow leaves the bow when it is released. So we went to the Great Salt Lake and shot the bow at an angle of 45 degrees. The arrow hit the ground at a distance of 600 feet. All of this was measured very roughly, but lets work with these figures, and, again, let's ignore air resistance. For simplicity let's also assume that the arrow is released at an initial height of 0 feet.
The arrow leaves the bow at a speed of miles per hour.
Note: My son and I did worry about the effect of air resistance. The arrows were sticking out of the sand where they had hit the beach. So my son shot another arrow downwards at an angle of 45 degrees straight into the sand. It penetrated to about the same depth as the arrows that had flown the distance. So they must have hit at about the same speed. We concluded that ignoring air resistance in this case was reasonable.
Hint: The speed of the arrow is measured in the direction in which it flies. The significance of shooting at an angle of 45 degrees is that initially the horizontal and the vertical components of the speed are equal. There are 3600 seconds in an hour and 5280 feet in a mile.