A player throws a football across the field. The equation h (x) = -16t^2 + 44t + 3.5 models the height, h, in feet, of the football as a function of time. t, in seconds. Ivan claims the football was thrown from an initial height of 3.5 feet with an initial velocity of 16 feet per second. Complete the statement to explain why ivan is incorrect

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facundo3141592 facundo3141592 · Answer 1 · 2020-11-20T01:28:55+01:00

Answer:

A quadratic equation for the height of an object is written as:

h(t) = a*t^2 + b*t + c

We can derivate it with respect to the time to get the velocity:

v(t) = 2*a*t + b

We can derivate it with respect to the time to get the acceleration:

a(t) = 2*a

Then:

a = half of the acceleration. (the gravitational acceleration for problems like this)

b = initial vertical velocity.

c = initial height.

In our case we have:

h(t) = -16t^2 + 44t + 3.5

-16 is half of the acceleration, we know that the gravitational acceleration is:

g = 32ft/s^2, and we have a negative sign because the gravity pullls the ball downwards.

44 is the initial vertical velocity of the ball (44ft/s)

3.5 is the initial height. (3.5ft)

Then the statement of Ivan is incorrect because the 16 does not represent the initial velocity