What Is the Longest Possible Hole-in-One for This Golfer?

AI Thread Summary
The discussion centers on calculating the longest possible hole-in-one for a golfer who hits the ball at an initial speed of 28.5 m/s, neglecting air resistance and assuming the tee and green are level. To determine the maximum range, the optimal launch angle must be identified, which is 45 degrees for maximum distance. The relevant equations for range and time of flight are provided, emphasizing the relationship between initial velocity, angle, and gravitational force. Additionally, the minimum speed of the ball during the shot is also a point of inquiry. Understanding these concepts is crucial for solving the problem effectively.
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A golfer gives a ball a maximum initial speed of 28.5 m/s. (Neglect air resistance.)
(a) What is the longest possible hole in one for this golfer? Neglect any distance the ball might roll on the green, and assume that the tee and the green are at the same level.
m
(b) What is the minimum speed of the ball during the hole-in-one shot?
m/s

How do you do this without a angle? (or for that matter any other information)
 
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(a) You need to find precisely the angle for the maximum range.

These equations might be a good help:

R = v_0\cos\theta t

\frac{t}{2} = \frac{v_0\sin \theta}{g}Do you understand how did I find them?
R = range
v0 = initial velocity
t/2 = time that the ball takes to reach the maximum height

Last hint: 2\sin\theta\cos\theta = \sin2\theta
 
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