Answer
Yes, the ball is a home run.
Work Step by Step
The x-value of the ball is given by
$x=x_0+(v_0 \cos \theta )t=400$
This implies,
$400=0(115 \cos 50^\circ )t$
or, $t=\frac{400}{(115 \cos 50^\circ )}=5.41$ s
The y-value of the ball is given by
$y=y_0+(v_0 \sin \theta )t-\dfrac{1}{2}gt^2$
This implies
$y=3+(115 \sin 50^\circ )(5.41)-\dfrac{1}{2}(9.8)(5.41)^2$
$y= 11.3 ft$
Thus, at time $t=5.41 s$ the y-position of the ball is 11.3 ft.
Also $11.3 ft \gt 10 ft$
Hence,
Yes, the ball is a home run.
