To attain the maximum range a projectile has to be launched at 45 degrees if the landing spot and the launch spot are at the same height (neglecting air resistance effects.)
Explain in a few sentences how the relation between the vertical and the horizontal components of the initial velocity affects the projectile range.

On the Moon the acceleration due to gravity is about one sixth that on Earth. If a golfer on the Moon imparted the same initial velocity to the ball as she does on the Earth, how much farther would the ball go?

Three swimmers start across the river at the same time. They all swim with the same speed relative to the water. Peter swims in a direction perpendicular to the current. Albert swims slightly upstream along a line which makes an 80 degree angle with the shore. Dawn swims slightly downstream along a line which makes an 80 degree angle with the shore. Which of the three swimmers reaches the opposite shore first?

The pilot of a small plane is trying to maintain a course due North. His air speed is 120 miles per hour. There is a 10 mph wind from the East. Estimate the direction in which the plane should be pointed to accomplish this.