Aball is thrown upward from a height of 880 feet above the ground, with an initial velocity of 96 feet per second. from physics it is known that the velocity at time t is v left parenthesis t right parenthesis equals 96 minus 32 t feet per second. a) find s(t), the function giving the height of the ball at time t. b) how long will the ball take to reach the ground

a)

b) It will take 11 seconds for the ball to reach the ground.

Explanation:

We have an initial height of 880 feet.

And

a) Find s(t), the function giving the height of the ball at time t

The position, or heigth, is the integrative of the velocity. So

In which the constant of integration K is the initial height, so

So

b) How long will the ball take to reach the ground

This is t when

So

This is t = -5 or t = 11.

However, t is the instant of time, so it has to be a positive value.

So it will take 11 seconds for the ball to reach the ground.

the area between the graph and the t axis

one "light year" is the distance that light travels, through vacuum, in one julian year.   that's 365.25 days, of 24 hours each.