Originally Posted by

**Kayla_N** 1. Evaluate the indefinite integral.

Let $\displaystyle u=5+14x^4\Rightarrow du=56x^3\,dx.$

2. A stone is thrown straight up from the edge of a roof,

feet above the ground, at a speed of

feet per second.

**A. **Remembering that the acceleration due to gravity is

, how high is the stone

seconds later?

Integrate the acceleration function to get the velocity function $\displaystyle v.$ You can solve for the constant of integration by noting that $\displaystyle v(0)=20.$

Integrate $\displaystyle v$ to get the stone's position function $\displaystyle s.$ Set $\displaystyle s(0)=775$ and you can solve for the constant of integration. Then just evaluate $\displaystyle s(3).$

**B. **At what time does the stone hit the ground?

That is, for what value of $\displaystyle t$ is $\displaystyle s(t)=0?$

**C. **What is the velocity of the stone when it hits the ground?

Evaluate the velocity function at the time found in part (B).