# Quiz 2 (Solution)

Date: MATH 1210-4 - Spring 2004

1. Find .

We can check the result: , as wanted.

2. Find the area determined by the -axis and the curve for .

Since for we can compute the area as :

3. 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 .
1. 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 .

2. 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 .

3. 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.

Javier Fernandez 2004-02-03