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

AI Thread Summary
The discussion revolves around whether John or Cory can achieve a hole-in-one from a tee elevated 4 feet, with the hole 250 yards away and 20 feet high. Cory hits the ball at 125 mph and John at 115 mph, both at a launch angle of 30 degrees. The parametric equations for their shots have been established, but the user is uncertain about the maximum height each ball reaches and whether either player can land directly in the hole without rolling. The key question is determining the necessary angle for the ball to hit the hole in one shot. The thread seeks assistance in solving these equations and understanding the physics behind the shots.
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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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?
 
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