Answer:
The rate of change of height with respect to time is -10.64 feet/sec
Explanation:
Given that,
There are three lines, so you can calculate three different values of the function at one time.
The function f(t) represents the height in feet of a ball thrown into the air, t seconds after it has been thrown.
Given table is,
Time t = 0, 1, 1,02
Function is,
We need to calculate the initial height of ball
Using equation of motion
Where, h₀ = initial height
u = initial velocity
t = time
g = acceleration due to gravity
At t = 0,
Put the value into the formula
We need to calculate the height of ball at t = 1
Using equation of motion
Put the value in the equation
Velocity is the rate of change of height with respect to time
So, velocity at 1.02 sec is given
We need to calculate the height
Using equation of motion
On differentiating w.r.to t
Put the value into the formula
Hence, The rate of change of height with respect to time is -10.64 feet/sec.