The height of a soccer ball that has been kicked can be modeled by the function

Question

The height of a soccer ball that has been kicked can be modeled by the function

h(𝑡) = −5𝑡2 + 20𝑡 + 1 , where h(t) is the height in metres and t is the time in seconds. Estimate the

instantaneous rate of change when t = 1 using the preceding and following method.

Answer 1

h(t) = -5t^2 + 20t + 1

v(t) = h'(t) =-10t + 20

v(1) = h'(1) = -10+20 = 10 meters per second

20t = vot where vo = the initial velocity

1 = ho = the initial height

-5t^2 is the effect of gravity

but -4.9t^2 would be more accurate or precise.

-5 means they rounded it off to nearest integer, but the gravitational deceleration is closer to -4.9t^2

-32 feet per second per second is the deceleration due to gravity. -32 feet = approximately -9.8 meters. half of -9.8 = -4.9