Number 10 part (d) only. I get a different answer than chegg solutions. Can you tell me if I am right or wrong?

10. Lunar projectile motion A rock thrown vertically upward from the surface of the moon at a velocity of 24m/sec (about 86km/h) reaches a height of s=24t0.8t2m in tsec. a. Find the rock's velocity and acceleration at time t. (The acceleration in this case is the acceleration of gravity on the moon.) b. How long does it take the rock to reach its highest point? c. How high does the rock go? d. How long does it take the rock to reach half its maximum height? e. How long is the rock aloft? A rock thrown vertically upward from ti.e surface of the mos at a velocity of 24m/sec (aboul 86km/h ) reaches a height of s=24t0.8t2m in sec. a) Find the roct's velocity at timet Find St v=dtds= Find ine rock's acceleration at time 1 Find dv/d a=dtdv= b) How long does if take the rock to reach its highest point? Set v(t)=0 and solve for t v=01.6+24=01.6t=24sec C) How high does the rock go? C)plugtS(t)aight=S(15)=15intoS=24t0.8t2=24(15)0.8(15)2=360180=180m Section 4 Numberio Continued d) How long does it tate the rock to reach half of its max height? Max Heisht =180 Half of Max Height =2180=90 S=24t0.8t2Sets=90andSolvetort s=9024t0.8t2=900=0.8t224t+90 0=0.8t224t+90 0=8t2240t+900 Mulfiplring thaough by 10 0=2t260t+225 Dividing throveh by 4 t=2(2)(60)(60)24(2)(225) Using the Quadratic q=46036001800 t=4601800 t=480060+302 t=430152