Calculating Ball Speed and Maximum Height

[jimmehx3]

Homework Statement

1. A ball is thrown upward. After reaching a maximum height, it continues falling back toward Earth. On the way down, the ball is caught at the same height at which it was thrown upward.
If the time (up and down) the ball remains in the air is 2.1 s, find its speed when it caught.
The acceleration of gravity is 9.8 m/s2 . Neglect air resistance.
Answer in units of m/s.

2. If the time the ball remains in the air is 2.23 s,
find the maximum height hmax the ball attained while in the air.
Answer in units of m.

Homework Equations

The Attempt at a Solution

 

[QuarkCharmer]

They mention that the ball is caught at exactly the same height as it was thrown. This forms a parabola. They give you the time that the ball was in the air (2.1) and the acceleration of gravity (9.8ms^2). From this you should be able to devise an equation to mark the balls height in respect to time (this is going to be a quadratic formula).

From there you can use the quadratic equation and formula for the vertex of a parabola to determine the max height of the ball.

This problem is very similar and should provide a good example:
http://answers.yahoo.com/question/index?qid=20071028093721AAI2vI1

And here is a great explanation of the application of this problem:
http://zonalandeducation.com/mstm/p...leMotion/generalSolution/generalSolution.html

 

[PhanthomJay]

Please show your relevant equations (hint: the kinematic motion equations ) and an attempt at a solution. What is the acceleration of the ball while in the air with no forces acting on it except gravity?