Vector Kinematics Application

Projectile motion is something we see everyday day in our lives, and a good example of this, is golfing. Many sports display projectile motion, such as football or basketball, but golf has always been a sport that I have enjoyed since I was a little kid, going to the driving range with my dad. Hitting a golf ball with a club creates a parabolic trajectory that is caused by the effect of gravity on the golf ball. We can calculate how far and how high a golf ball will travel, using the principles of projectile motion.

The initial velocity of the golf ball has a vertical and horizontal component. The initial vertical and horizontal components can be found if we know the angle the golf ball was hit, using the equations: Vo horizontal=Vo cos θ and Vo vertical=Vo sin θ, Vo being the speed with which the club hit the ball. The launch angle affects the vertical and horizontal components as seen in the equations above, therefore the launch angle can affect how high the ball will travel, and how far it will travel.

http://sportsnscience.utah.edu/the-in-depth-science-of-golf/

Due to gravity, there is a downward (vertical) acceleration, however, there is no horizontal acceleration, therefore, Ax=0, and Ay=-9.8m/s^2. This means that the horizontal component is moving at a constant velocity. With the horizontal acceleration being 0, the range, or the horizontal distance the ball travels, can be calculated using the equation, Dx=V horizontal × t (time of flight). However, the vertical motion is different as we have to deal with an acceleration due t =o gravity. The vertical component of the initial velocity is upwards, however we have to account for gravity, which is pulling the ball towards the ground, therefore we use the formula, Dy=Vo(y) × t + 1/2 at^2 to find the vertical distance the golf ball travels.

Air resistance, and wind can play a significant role on the trajectory of a golf ball, however this explains why golf balls have dimples to reduce these affects. Although we usually do not account for air resistance in problem solving, this diagram shows an interesting fact that I have learned through this journal entry.

http://io9.com/5606110/why-golf-balls-have-dimples

Projectile motion can be seen almost anywhere, but golf is a sport that solely relies on the trajectory of the ball and where is lands, which really shows the importance and application of projectile motion.