Confusion about Instructor's solution of HRK

[phymath7]

Homework Statement

This is an excercise from the book 'Physics' by HRK:A batter hits a pitched ball at a height 4.0 ft above the ground so that its angle of projection is 45° and its horizontal range is 350 ft. The ball travels down the left field line where a 24-ft high fence is located 320 ft from home plate. Will the ball clear the fence? If so, by how much?

Relevant Equations

$y-y_0=xtan\theta-\frac {gx^2}{2v_0^2cos^2\theta}$

The instructor's solution goes like this:
The initial speed of the ball is given by $v_0=\sqrt{gR}$ where R is the range.But this is true if the final position of the projectile is y=0 but in this case, y=-4.Though this doesn't affect much in this case,but for higher velocity and extreme cases this certainly would.Am I right?

 

[TSny]

Yes, you are right.

 

[phymath7]

Yes, you are right.

Then it's a pity that this solution manual contains such basic error.

 

[TSny]

Then it's a pity that this solution manual contains such basic error.

Perhaps the solution in the manual interprets the horizontal range R (350 ft) to be the horizontal distance that the ball would travel before it returns to its initial height of 4 ft above the ground (assuming the ball clears the fence). Then, $v_0 = \sqrt{gR}$ is OK. I'm not defending this interpretation, but it might be what was going on in the mind of whoever wrote the solution. Who knows. I'm with you in interpreting the horizontal range as the horizontal distance traveled until landing on the ground.

It's fairly common for solution manuals to have occasional errors.