writing functions

Question

The height (feet) above the ground of a golf ball depends on the time, t (in seconds)it has been in the air. Ed hits a shot off the tee that has a height modeled ny the function f(t)=-16t^2 + 80t. Sketch a graph and create a table of values to represent this function.    How long is the golf ball in the air?  What is the maximum heightof the ball? How long after it is hit does the ball reach the maximum height?

Answer 1

Using vertical movement against gravity

 

h= ut -1/2(gt² )

 comparing with the function given 

 f(t) = 16t² +80t

      = 80t + 16t²

this gives u = initial veocity = 80ft/sec

 g = -32ft/sce²   - sign due to upward motion

 

using V² = u² +2gh

 

         0= u² - 32h

u²  = 80x80 = 32 h

 

gives h= 6400/64 = 100ft (Ans)

 

for time in air

v = u +gt

v=0 at highest point

u-32 t =0

80= 32 t

t= 80/32=2.5 sec Time the ball remains in air (Ans)

The time ball is in air =2.5+2.5 = 5 Sec. (up and down time)  (Ans)

The shape of the graph will be a parabola

y= 16x² +80x passing through origin