Quadratic Word Problems

Question

At a swim meet, Janet dives from a diving board. Her position above the water is represented by the equation h(t) = -16t^2+24t+40, where t represents the time in seconds at h(t) represents the height in feet.

a.After how many seconds does Janet enter the water?

b. What is the greatest height Janet reaches in her dive?

Answer 1

The student who submitted this problem indicated being in Algebra I. As a result, the use of derivatives would not be an option here.

Algebra I and II students normally have been shown that the maximum or minimum occurs when x= -b/a/2 for a quadratic in the form f(x) = ax² + bx + c.

In this case, that would be x = -(24)/(-16)/2 = 3/4, the same number that the derivative provides.

Answer 2

h(t) = -16t^2 +24t +40

= 0 = 2t^2 -3t - 5

=(2t -5)(t+1) = 0

2t-5 =0

t= 5/2, ignore the negative solution t=-1

t= 2 1/2 seconds to splash down

greatest height is when v=h'=0= -32t +24

t = 24/32 = 3/4

h(3/4) = -16(3/4)^2 +24(3/4) +40

= -9 +18+40

= 49 feet = max height