Which expression could represent the height of a soccer ball as it is in the air after being kicked?(1 point) A. −16t2+4t3 B.9t2+25t C.−16t2+25t+1 D.−16t+9

Option C

Step-by-step explanation:

When an object is in the air, the only force acting on the object will be the gravitational force, so the only acceleration acting on the ball is the gravitational acceleration:

a(t) = -32ft/s^2

Now, for the velocity we integrate over time, and get:

v(t) = ( -32ft/s^2)*t + V0

where V0 is the initial vertical velocity, that it depends on how the ball was kicked.

For the position we integrate again over time:

p(t) = (1/2)*( -32ft/s^2)*t^2 + V0*t + p0

Where p0 is the initial position.

p(t) = (-16ft/s^2)*t^2 + v0*t + p0

Then the only option that fits this model is:

C: -16*t^2 + 25*t + 1.

the answer is 8/21

hope this