Solve Quadratic Function

Question

question : Create quadratic function to model the height of an object thrown into the air with the following conditions: max height is 95m, object starts on the ground, object takes 10s before returning to the ground.

Answer 1

max height = 95 meters, above ground level

ho = 0= ground level

10 s = 10 seconds up and down from start to finish, ground level to ground level again

5 s to reach max height = 95 m,

5 seconds = half the total object flight time of 10 seconds

general equation is

h(t) = (a/2)t^2 +vot +ho

where a=acceleration due to accepted value of the effect of gravity =-9.8 m/s^2

(that's a very close approximation of the force of gravity, on earth at sea level., with normal atmosphere. You could do this problem with a better more accurate approximation, but almost no one does.)

h(t) = -4.9t^2 +vot +ho,

h(t) =-4.9t^2 +vot +0

ho = 0 for ground level= initial height

vo = initial velocity in meters per second

t= time in seconds

h = height in meters = 95 meters when h=max, h=0 initially

take the 1st derivative of the h(t) function and set it equal to zero:

h'(t) = v(t) = -9.8t + vo = 0

at max height

t = vo/9.8 = 5

vo = 9.8(5) = 49 m/sec = initial velocity

h(t) = -4.9t^2 +49t

is the quadratic function modeling the height of the object, when max h=95 m and total flight time =10 s