Max Height of Ball: Can it be Determined?

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SUMMARY

The maximum height of a baseball hit by a batter cannot be definitively determined due to the lack of information regarding the angle of projection. The discussion highlights that while the total mechanical energy remains constant, the vertical component of velocity at the peak is zero, but the horizontal component remains unknown. The official conclusion states that without the angle of projection, calculating the maximum height is impossible.

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Homework Statement



A batter at a baseball game hit a ball such that it flew into the stands. The ball was caught by a fan when it was moving at 10 m/s at a height 20 m above the height it was hit. What was the maximum height to which the ball rose before falling back down towards the fan?

2. The attempt at a solution

The official answer is "The maximum height cannot be determined. "
I thought it could be determined by noting that the total mechanical energy is the same at the max height, 0 m/s equaled the energy at 20 m, 10 m/s.
What am I missing?
 
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No, the velocity at the top is not 0 m/s, that is only the vertical part of the velocity, the horizontal part is a constant and we don't know any angle here so we can't distinguish the two.
 
You're a genius! Thanks!
 

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