Can either golfer hit a hole in one with this velocity and angle?

In summary, John and Cory are golfing on a hill with a 4-foot elevation and trying to hit a hole located 250 yards away and 20 feet above the horizon. With John hitting at 115 mph and Cory at 125 mph, the question is whether either of them can hit a hole in one without rolling or bouncing. To find the answer, parametric equations are used to calculate the horizontal and vertical distance of the ball based on time. After graphing the equations, a suitable angle (theta) needs to be found in order to hit the hole in one.
  • #1
aywoo401
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So I'm having a tough time figuring out this problem.

John and Cory are golfing in the DV golf ball team. They are teeing off a hill 4 feet above the horizon. The hole is located 250 yards from the tee. The hole is 20 feet above the horizon. Cory is stronger than John and hits a velocity of 125 miles per hour, while John hits it at 115 miles per hour. Graph the ball when pheta equals 30 degrees.

Does either player have a chance of hitting a hole in one without rolling or bouncing?
I said "no" but I'm not sure exactly why or how...

What was the maximum height of each ball?

[When a person hits a ball at h feet above the ground, it travels at an angle of pheta with the ground. The intial velocity is in feet per second.]
X gives horizontal distance in feet terms of time.
Y gives vertical distance in feet in terms of time/

X = (v0 cos(theta))t and y = h + (v0 sin(theta))t - 16t^2


These are the parametric equations I've set up:
John: X=(168.6cos30)T; Y= 4+(168.6sin30)T-16T^2
Cory: X=(183.3cos30)T; Y= 4+(183.3sin30)T-16T^2

I graphed both equations but now I'm stuck on what else to do. Any help or hints would be appreciated. :]
 
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  • #2
For the question of if either of them can hit a hole in one without rolling or bouncing, what do you think the x and y coordinates should be for the ball when it lands? Can you find a theta that will give you these coordinates? It's the same question as, what angle should the ball fly off with so it will hit a hole in one?
 

1. What are parametric equations?

Parametric equations are a set of equations that express a set of variables in terms of one or more independent variables, known as parameters. They are commonly used in mathematics and physics to describe the motion of objects.

2. How are parametric equations different from regular equations?

The main difference between parametric equations and regular equations is that in parametric equations, the variables are expressed in terms of parameters, while in regular equations, the variables are expressed in terms of each other. This allows for more flexibility in describing complex motions and curves.

3. What is the purpose of solving a parametric equations problem?

The purpose of solving a parametric equations problem is to determine the values of the parameters that satisfy the given set of equations. This allows us to understand and predict the behavior of objects in motion or to find the solutions to other mathematical problems.

4. What are some common applications of parametric equations?

Parametric equations are widely used in physics, engineering, and computer graphics. They are commonly used to describe the motion of objects, such as projectiles and planets, and to create complex curves and shapes in computer graphics.

5. What are some strategies for solving a parametric equations problem?

Some common strategies for solving a parametric equations problem include eliminating the parameter by substituting one equation into the other, graphing the equations to find the points of intersection, and using trigonometric identities to simplify the equations. It is also helpful to carefully identify and label the given parameters and variables before attempting to solve the problem.

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