A gymnast dismounts the uneven parallel bars. Her height, h, depends on the time, t, that she is in the air h = −162 + 24t + 16. How long will it take the gymnast to reach the ground?
that is when h=0 so assuming yo meant h(t)=-16t²+24t+16 solve for t such that h(t)=0 because when height=0, the gymnast hits the ground
so 0=-16t²+24t+16 using math (imma complete the square 0=-16(t²-3/2t)+16 0=-16(t²-3/2t+9/16-9/16)+16 0=-16((t-3/4)²-9/16)+16 0=-16(t-3/4)²+9+16 0=-16(t-3/4)²+25 -25=-16(t-3/4)² 25/16=(t-3/4)² sqrt both sides +/-5/4=t-3/4 3/4+/-5/4=t if we do plus (because minus would give us negative height) 8/4=t 2=t it takes 2 seconds
