Monday, November 27, 2017

Presidential trajectory

Warning: political satire follows

In a recent news story, President Trump said that he was going golfing with Tiger Woods and others, but would play 'quickly' so he could get back to work on, you know, our country. Of course, I couldn't help but think of precisely how quickly he could complete the 18 holes at Trump National Golf Club. This brought me to some kinematical considerations.

Now, according to some brief and extremely reliable google searching, I found that Tiger Woods can swing his driver around 120 mph, giving the golf ball a speed of about 195 mph. Let's assume the POTUS is a better golfer than Woods, and in fact the best golfer ever, so he can give the ball a speed of 200 mph. Converting this to meters per second, we find he hits the ball with an initial linear velocity of 89 m/s. While we're at it, let's convert this to rotational velocity using the average radius of a golf ball, 42.67 mm; we find the ball is rotating at 2086 rad/s, or 332 rev/s. Wow!

Before continuing, let's make some more assumptions, since truth is subjective anyway: President Trump hits the ball every single time at an angle of 30 degrees from the horizontal, and scores a hole in one on every drive. I mean he's the best, why question it?

According to the website, the course is 7,693 yards long, or 7,034 meters. Using our classic kinematic equation, we find the time it takes for the golf ball to reach the peak of its trajectory: v initial, y=89sin(30) m/s; v final, y=0 m/s; a, y=-9.8 m/s^2 and v final=v initial+(a)(t). The time it takes is thus determined to be 4.5 s, and therefore 9 s for the complete trajectory. We find that the ball covers (89cos(30)m/s)(9 s) horizontal distance, which calculates to 694 meters. The ball also went through 2988 revolutions during this time. Huge!

If it took 9 s for the ball to travel 694 meters, we can easily determine that it would take only 91 seconds for the Commander in Chief to complete the golf course. The news report saying it would be quick certainly wasn't fake news!

Except, of course, it would take him a total of over 4 hours to travel the distance of the course if he consistently walked at the sluggish pace of 1 mph, or .447 m/s. Hopefully they have a golf cart, so our President can get right back to making the country great again!

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