Max height given angle and distance

[agentnan]

Good morning,

I am trying to set up the following problem:

A golfer hits a golf ball at an angle of 25.0 degrees to the ground. If the golf ball covers a horizontal distance of 301.5 m, what is the ball's maximum height? (Hint: At the top of its flight, the ball's vertical velocity component will be zero).

I keep coming back to needing to know either time &/or the initial velocity.

Can it be assumed that the maximum height will occur at half the distance of X? If it can, I could use:
tan25 = max height of Y / divided by .5X
this would give me a solution for the max height of 70.30. Unfortunately this answer is wrong. According to the book the answer is 35.1m, so I gather I can't do this...

I then tried based on the hint to use the formula for the final velocity in the y direction as 0, but in both formulas which involve the final velocity in the y direction I would need to know the initial velocity which I do not have. To find the initial velocity I would need the time. In all the formulas involving initial velocity or time, I am missing at least 2 factors, so I do not see a way to solve for either of them.

I am sure I am missing some facet of this question. Any guidance would be appreciated.

 

[agentnan]

please disregard...I just found a range formula for X that was later in the chapter which I can use. (change in X = initial velocity X sin 2a / g ) . Thanks for your help in this matter!