Solve the Problem

Question

When you leap up from a small hill that is 10feet above the surface of the Planet X, your height above the surface after t seconds is given by the function h(t)=-12t^2 +48t+10 where height is measured in feet.

a) Find h(1), h(2)?

b)How high off of the surface do you get?

c)How long does it take to attain this maximum height?

Answer 1

(a) h(1) = -12(1)+48(1)+10=46

h(2)=-12(4)+48(2)+10=58

(b) This function is a parabola facing down. Put it into standard form to get the vertex:

h(t)=-12t²+48t+10= -12(t²+4t-5/6)

Complete the square = -12(t²-4t+4-4-5/6)=-12(t-2)²+48+10

So h(t)-58=-12(t-2)² so the vertex is (2,58). Therefore, maximum height is 58 feet and (c) one reaches that height after 2 seconds.

For those who know calculus, you can differentiate h(t) and set the derivative -0 to solve for 2 at maximum height (same answer, of course).