Answer:
The maximum height, rounded to the nearest foot is 12,469ft.
Step-by-step explanation:
The time it takes for the rock to reach maximum height is when
[tex]v-gt =0[/tex]
[tex]t = \dfrac{220ft}{9.8ms^{-2}} \\\\t = 2.45s[/tex]
Now, the vertical displacement [tex]y(t)[/tex] of the rock is given by the function
[tex]y(t)=vt-\dfrac{1}{2}gt^2 +h_0[/tex],
where [tex]h_0[/tex] is the height of the mountain . Putting in the numbers we get:
[tex]y(t)=220t-\dfrac{1}{2}(9.8)t^2 +10,000[/tex]
[tex]y(t)=220t-4.9t^2 +10,000[/tex]
Now, when the rock reaches its maximum height at [tex]t =22.45[/tex], we have
[tex]y_{max}=y(t)=220(22.45)-4.9(22.45)^2 +10,000[/tex]
[tex]\boxed{y_{max} = 12,469ft}[/tex]
which is the maximum height the rock reaches.
