$26-$ A circus acrobat is launched by a catapult at a speed of $15(\frac{m}{s})$ at an angle of $=$ abeve the horizantal as shown. At a distance of $20$ m awoy, her partner is standing on a platform at a heigh of hm meter At the instont that the acrobat is lounched, her partner throws a basketball towerds her herijantally at a speed of $5(\frac{m}{s}).$

a$)$ Write equations for the horizantal and vertical positions as a function of time fer both the acrobat and the basketball. $($Be consistent in your choice of orgyin$)$

When will the performer and bosketball be at the same horijantal position?

c$)$ Find the value of $h$ for which the acrobat will catch the ball. Assume that she and the ball must be at the same herght for her to catch it$.$