Question

A diver on a platform 40 feet in height jumps upward with an initial velocity of 5ft/s. His height in h feet after t seconds is given by the function h=-16t^2+5t+50.

a. What is his maximum height? I got 50.39

b. How long will it take him to reach the surface of the water?

h=-16t^2+5t+50
50.39 = -16t^2+5t+50
-16t^2+5t+50 = 50.39

I am going to try completing the square.
(-16t^2/16)+(5/16)t = 0.39/16
t^2 + (5/16)t = .02

I'm stuck.

Answer 1

Is the platform really 40 feet in height, not 50 feet...? Anyway,

a. Yes, that value is right.

b.
Time it takes from platform to maximum height (I used derivatives):
dh/dt = -32t + 5
0 = -32t + 5
t = 0.15625 s

Time it takes from maximum height to surface of water:
h = vo*t - (1/2)*g*t^2
But vo = 0 because it's freefall, and g = 32.2 ft/s^2:
50.39 = 0 - (0.5)*(-32.2)*(t^2)
50.39 = 16.1(t^2)
t^2 = 3.1298
t = 1.769 s

Total time: 1.769 + 0.15625 = 1.925 s

hope this helps~ `u`