A dive is the equation h=13t2-5t where h is the height above the water in meters and t is the time in sec.How long does it take for the dive to the surface?What is the maximum depth the it get to?

Question

pls help!!

Answer 1

h=13t²-5t. This can be written h=13(t²-5t/13)⇒h=13(t²-5t/13+(5/26)²-(5/26)²).

h=13(t-5/26)²-25/52. In this form it’s possible to see that when t=5/26=0.19 sec, approximately, the maximum depth is 25/52=0.48m approx, because all other values of t make h less negative, i.e., the diver is closer to the surface. And when h=t(13t-5)=0 (on the surface) t=0 (initial condition on commencement of the dive) and t=5/13=0.38 seconds, which is twice the time it took to reach maximum depth.