Hello, mj.alawami!

A boy kicked a football with an initial vertical velocity component of 15.0 m/s

and a horizontal velocity component of 22.0 m/s.

a) What is the velocity of the football (magnitude and direction)?

The velocity can be represented by this triangle: Code:

*
* |
* | 15
* θ |
* - - - - - - - *
22

The magnitude of the velocity is the length of the hyptenuse.

. . m/s.

The direction of the velocity is given by:

. .

b) How much time is needed to reach the maximum height?

The height of the football is given by: .

The graph is a down-opening parabola which reaches its maximum at its vertex.

The vertex is at: .

The ball reaches maximum height in abut 1.5 seconds.