With the assumptions that you make, the golf ball is basically free falling without losing horizontal speed and is therefore described by a parabola: y = − a x 2 + b x + c, where x is the horizontal distance and y is the height of the ball.
What is the average width and height of a golf ball?
The average width and height of a golf ball is (43 mm). Golf balls are certainly not all created equally. In fact you’ll find some that are bigger than the standard 1.68 inch size. Going back decades ago, there use to be 2 official golf ball sizes.
How is the distance of a golf ball determined?
Using image analysis, the ball's launch conditions are determined and fed into a model that—based on an optimization problem—predicts the total distance the ball will travel. The Rules require that this distance be no more than 317 yards.
How do you find the volume of a golf ball?
To measure the volume of a golf ball we take the radius of 0.83 inches, and then calculate this value based on sphere volume. We get an answer of 2.482 (cu in) | 40.677 (cm3).
How far should you hit a golf ball?
Choose the club you would normally hit from 144 yards away. Consider the temperature and humidity, notes Langer. The ball won't travel as far in cool weather or humid weather.
How do you find the maximum height of a ball?
Use the vertical motion model, h = -16t2 + vt + s, where v is the initial velocity in feet/second and s is the height in feet, to calculate the maximum height of the ball.
What is the formula for finding maximum height?
h = v 0 y 2 2 g . This equation defines the maximum height of a projectile above its launch position and it depends only on the vertical component of the initial velocity.
How is golf ball trajectory calculated?
Fzw = Fw cos y = -sin y (Cwvw) If there is any side spin on the ball - and there usually is - then the ball will curve in the direction of the spin. Side wind will, of course, cause the ball to curve in its direction and head or tail wind will affect the ball's carry.
How do you find maximum height with velocity and mass?
2:165:20Calculating height when you only know an object's final velocityYouTubeStart of suggested clipEnd of suggested clipTimes the mass multiplied. By V squared.MoreTimes the mass multiplied. By V squared.
What is the free fall formula?
vf = g * t where g is the acceleration of gravity. The value for g on Earth is 9.8 m/s/s. The above equation can be used to calculate the velocity of the object after any given amount of time when dropped from rest.
How long does the ball take to reach its maximum height?
How long do you have to get out of the way before the cannonball comes back down and obliterates your new cannon? It takes about 88 seconds for the cannonball to reach its maximum height (ignoring air resistance). You have 176 seconds, or 2 minutes and 56 seconds, until the cannonball destroys the cannon that fired it.
How is math used in golf?
In many cases, math is used to place limitations on golf equipment, such as restricting the distance the ball will travel, as predicted by mathematical models. The Rules also place limits on a value called the coefficient of restitution, which measures the efficiency of the impact between a club and ball.
What is the formula for calculating projectile motion?
Projectile motion equationsHorizontal velocity component: Vx = V * cos(α)Vertical velocity component: Vy = V * sin(α)Time of flight: t = 2 * Vy / g.Range of the projectile: R = 2 * Vx * Vy / g.Maximum height: hmax = Vy² / (2 * g)
How do you derive the equation of trajectory?
Answer. 1) The path of the projectile is shown in the figure. The horizontal component of velocity always remain same as there is no acceleration on the horizontal axis. The vertical distance travelled by projectile is given from kinematical equation s = ut + ½at2.
How do you calculate height change?
0:052:51Gravitational Potential Energy Part 3 - Calculating Height - YouTubeYouTubeStart of suggested clipEnd of suggested clipPotential energy divided by mass times the acceleration due to gravity and as G PE divided by MMorePotential energy divided by mass times the acceleration due to gravity and as G PE divided by M times G.
How do I find the height of an object?
The height of an object is calculated by measuring the distance from the object and the angle of elevation of the top of the object. The tangent of the angle is the object height divided by the distance from the object. Thus, the height is found.
How do you find height given mass and time?
1:236:27GCSE Physics exam calculations: using mass and height to find final ...YouTubeStart of suggested clipEnd of suggested clipJust before it hits the ground.MoreJust before it hits the ground.
Step 1
Take your tee shot as per normal, and then find your ball and stand directly beside it.
Step 2
Turn on the range finder, hold its sight to your eye and aim it directly at the flagstick. All range finders work slightly differently, but always include a sight that you aim at the flag. Note the reading on the range finder that indicates your distance from the flag.
Step 3
Subtract the distance to the flagstick from the total yardage of the hole. For example, if the hole is 380 yards from the tees that you played and the range finder indicates that you're 120 yards from the flag, you hit your drive 260 yards.
Step 2
Pace off the distance to the nearest yardage marker. Yardage markers are situated throughout each hole and provide golfers with numbers indicating how far they are from the front or center of the green.
Step 3
Subtract the yardage to the green from the total yardage of the hole. For example, if the hole is 175 yards and you're close to the 50-yard marker, you hit your tee shot 125 yards. Most courses have markers every 50 yards.
How much to deduct for golf shots at high altitude?
Although the general rule is to deduct 10 percent to determine the "true" distance for shots to the green at high altitude, it's not a rule you can bank on. As "Golf Digest" put it, the 10 percent rule, even for the professionals, is "more of a ballpark figure than an exact science.".
Why does the ball fly farther at high altitudes?
The ball flies farther at high altitudes: The air is less dense, so there is less friction to slow the orb's forward motion.
Can a golf ball travel in cool weather?
Consider the temperature and humidity, notes Langer. The ball won't travel as far in cool weather or humid weather. It will travel farther in warm weather and when the air is dry.
How many golf balls are on the conforming list?
Currently, there are approximately 1200 golf balls on the official conforming list, and each one must be resubmitted for evaluation each year.
What is the official rule of golf?
Credit: NASA. (Phys.org)—The official Rules of Golf, which are continually being revised and updated as new equipment emerges, have close ties to mathematics. In many cases, math is used to place limitations on golf equipment, such as restricting the distance the ball will travel, as predicted by mathematical models.
How far can you drive a golf ball at sea level?
If you normally drive the ball 250 yards at sea level, you will likely drive it 265 yards in Reno. The golf ball does not spin any less at high elevation. However, because the air is less dense and imparts less force on the ball, the lift force is also lower.
Why does a golf ball fly at high altitudes?
The golf ball flies further in high altitudes mainly due to the change in air density, which decreases as elevation increases. Thinner air exerts less drag force on the ball. The ball moves more easily through the air and doesn't slow down as quickly as it flies, resulting in greater distance.
What is a hook in golf?
A hook or slice is generated when the ball's spin axis is tilted and the lifting force pulls a little to the left or right (as a result of the golfer imparting some amount of sidespin to the ball) instead of straight up.
What is the effect of the spin of a ball on the trajectory of an airplane?
Thus, at higher elevations the trajectory is less influenced by lift, and thus has a "flatter" shape and a more glancing impact with the ground.
What is the lifting force of a 5,000 ft slice?
At 5,000 ft elevation, the air density is about 14% lower than at sea level, so the lifting force is also about 14% less and the hook or slice will curve about 14% less .
Why is gravity reduced at higher elevations?
The notion of reduced gravity at higher elevations is technically true, because the strength of gravity decreases with increased distance from the center of the Earth. When playing golf in Denver, for example, we are about a mile farther from the center of the Earth than we are when playing in Los Angeles.
Does golf slow down as fast as it flies?
Thus, it doesn't slow down as quickly as it flies, resulting in greater distance. Since golf shots vary widely in their launch conditions (the initial speed, spin rate, and launch angle of the ball), the effect will vary greatly depending on the golfer and what club is being used.
Homework Statement
A golf ball is hit with a velocity of 22.8m/s at an angle of 40.0° with respect to the horizontal.
The Attempt at a Solution
I am unsure of which equations to use in this problem but I've attempted something that I think may be right but would greatly appreciated if someone could just check my answers and correct me if necessary and explain which equations you use if applicable.
Answers and Replies
You have done a) correctly, but b) is not correct. To work out the max height of the ball, first think about the ball's motion, at what stage in its journey will it be at its highest point?
When to hit golf balls farther?
Golfers will hit it farther when the temperature is warmer (both the air, the club and the ball), when the wind is following (tail wind), when the target is downhill and when altitude is high. GOLF TIP: During cooler weather, keep your golf balls warm.
How to warm up trouser balls?
Keep 2 in your trouser pockets to keep them warm. Replace the cold ball with a warm one at the end of the hole . Place the cold one in your pocket to get warmed up again.
Can you roll golf in the wet season?
During the wet season, there isn't much roll. GOLF TIP: During the cooler wet season, play the forward tees to shorten the course. This way, you'll be the same distance from the green as in the summer when you play longer tees.
Can you get a golf ball warmer?
You can even get a golf ball warmer to keep more balls warm! The total distance of a drive depends on how far the ball carries in the air and then how far it rolls along the ground. The roll distance is highly dependent on the hardness of the ground and on the trajectory angle of the ball at impact.