*Date:* MATH 1210-4 - Spring 2004

- Find
.

We can check the result: , as wanted.

- Find the area determined by the -axis and the curve
for
.
Since for we can compute the area as :

- A ball is thrown straight up from the top of a tall
building with an initial velocity of . The acceleration due
to the gravity force is
.
- Find a formula for the velocity of the ball seconds after
it is thrown.
Since we have . But we know that , so that and we have .

- Find a formula for the position (height above the ground) of
the ball seconds after it is thrown.
We denote the height above the ground after seconds with . Then, since we have . Additionally, , so that and the final formula is .

- What is the maximum height that the ball reaches?
The time of the maximum height satisfies . That is, , so that .

The position at , the maximum height, is ft above the ground.

- Find a formula for the velocity of the ball seconds after
it is thrown.

Javier Fernandez 2004-02-03