Answer:
(a): s(t)= hi + Vo * t - g* t²/2
(b): Will take the ball to reach the ground t= 11 seconds.
Explanation:
hi= 880 ft
Vo= 96 ft/s
g= 32 ft/s²
equating to 0 the equation of s(t) and clearing t, we find the time it takes for the ball to fall to the ground.
Answer:
a) [tex]s(t) = 96t - 16t^{2} + 880[/tex]
b) It will take 11 seconds for the ball to reach the ground.
Explanation:
We have an initial height of 880 feet.
And
[tex]v(t) = 96 - 32t[/tex]
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
[tex]s(t) = \int {(96 - 32t)} \, dt[/tex]
[tex]s(t) = 96t - 16t^{2} + K[/tex]
In which the constant of integration K is the initial height, so [tex]K = 880[/tex]
So
[tex]s(t) = 96t - 16t^{2} + 880[/tex]
b) How long will the ball take to reach the ground
This is t when [tex]s(t) = 0[/tex]
So
[tex]s(t) = -16t^{2} + 96t + 880[/tex]
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.
