After catching the ball, Sarah throws it back to Julie. The ball leaves Sarah's hand a distance 1.5 meters above the ground, and is moving with a speed of 15.0 m/s when it reaches a maximum height of 10.0 m above the ground.
What is the speed of the ball when it leaves Sarah's hand?

distance between the two girls= 32.5

How did you get the disatnce between the girls = 32.5m? That's inconsistent with the data given in the question.

You need to determine the vertical component of initial velocity that allows the ball to rise a total 8.5 meters. You can use v^2 = 2gh for that calculation. Then do vector addition of that vertical component with the given horizontal component of velocity to find the total initial velocity.