Finding the Initial Speed for a Winning Putt at the U.S. Open

In summary, the problem is trying to determine the initial speed needed to make a 22.0 ft putt in the U.S. Open, given that an initial speed of 1.27 m/s stopped the ball 6.00 ft short of the hole. Using the kinematic acceleration equation, it can be determined that the deceleration caused by the grass is 0.3301 m/s^2. However, the calculation to find the correct initial speed is incorrect and further assistance is needed.
  • #1
XPX1
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At the 18th green of the U. S. Open you need to make a 22.0 ft putt to win the tournament. When you hit the ball, giving it an initial speed of 1.27 m/s, it stops 6.00 ft short of the hole.


(a) Assuming the deceleration caused by the grass is constant, what should the initial speed have been to just make the putt?
m/s


(b) What initial speed do you need to just make the remaining 6.00 ft putt?
m/s

So far, to try and find the inital speed needed to make the putt, I have done the following.

1. 22 feet away from the hole, the putt is 6 feet short, so I subract 6 from 22, and I get 16 feet.

2. Now that I have 16 feet, I take the initial speed of 1.27 m/s and convert it to feet per second. I get 4.166666673 feet per second.

3. Now that both the feet away from the hole (16 feet) and the initial speed (4.166666673 ft/s) are in the same units, I divide them, to get the time it took for the golf ball to travel that distance. I get 3.839999994 or 3.84.

4. Now I am stumped, with these things I have figured out about the problem, how can I use this to find the inital speed I would need to just make the putt?

Time it takes golf ball to travel 16 feet away from the hole (3.84 seconds)
Total Distance = 22 Feet
Golf Ball = 6 feet short from hole

as for question (b) I am completely stumped. Any help would be greatly appreciated! Thank you!
 
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  • #2
I don't think your step -3- is correct. The velocity is not constant, the deceleration is. Use the kinematic acceleration equation to tell you what the deceleration is in m/s^2.
 
  • #3
the correct formula is Change in Velocity / Time correct? If So I have taken the change in velocity, I have taken 1.27 m/s and divided it by 3.84(the time taken for the ball to reach the hole)

This gives me the number .330729167 or, .3301

When I plug this into a position versus time graph, I get

xf=xi+viT+.5at^2

0=1.27+0+.5(.3301)t^2


0=1.27+.1653645833 or

0=1.27+.17t^2

now I subtract

0=1.27+.17t^2
-1.27

-1.27=.17t^2

t^2=-.1338582677 (or -.134)

but I cannot get the square root of -.134 on my calculator because it says ERROR: NON REAL ANSWER, so I am not sure where I messed up, but any help is still appreciated!
 
  • #4
****Bump****
 

Related to Finding the Initial Speed for a Winning Putt at the U.S. Open

1. What is initial speed?

Initial speed is the speed at which an object is traveling at the start of its motion. It is also known as the initial velocity.

2. How is initial speed different from final speed?

Initial speed is the speed at the beginning of an object's motion, while final speed is the speed at the end of an object's motion. Final speed can also be referred to as the object's velocity at a certain point in time.

3. How is initial speed calculated?

Initial speed can be calculated by dividing the total distance traveled by the total time taken. It can also be calculated by multiplying the acceleration of the object by the amount of time it has been accelerating.

4. Why is initial speed important in physics?

Initial speed is important in physics because it is a key factor in determining an object's motion and the forces acting upon it. It is also used to calculate other important variables such as acceleration and final speed.

5. Can initial speed ever be equal to final speed?

Yes, initial speed can be equal to final speed if the object has constant velocity and does not experience any acceleration. This is known as uniform motion.

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