h(t)=-16t^2+15t+12 (e) maximum height is reached when h'(t)=-32t+15=0, or tm=15/32 seconds. maximum height reached = h(tm)=h(15/32)=-16(15/32)^2+15(15/32)+12 =993/64 ft =15.516 ft. (f) when Greg reaches water, h(t)=0=-16t^2+15t+12 Solve for t using quadratic formula, t=[-15+/- sqrt(15^2+4*12*16)]/(2*-16) =-0.516s or 1.4535s. Reject negative root so Greg reaches water at t=1.4535 seconds.
