# Find max distance of football thrown while running.

1. Sep 11, 2016

### connor67

1. The problem statement, all variables and given/known data
A baseball player always throws a fastball at a speed of 40.26 m/s. What is the maximum distance, in meter, this player can throw the ball while running toward his teammate who catches the baseball at the same height as he throws at, assuming that this player runs at a speed of 5.51 m/s?

2. relevant equations
y = yi +Vyi*t-(g*t^2)/2
x = xi +Vxi*t
i think t = (2Vi*sin(theta))/g

3. attempt
i do not know how to find the angle for max distance. i believe the x component for velocity is 5.51+(40.26)cos(theta). the y would be (40.26)sin(theta). Would i turn it into <5.51+(40.26)cos(theta) i, (40.26)sin(theta) j> or what would i do from here? if this is wrong please let me know. any help would be appreciated.

Last edited: Sep 11, 2016
2. Sep 11, 2016

### BvU

Hi Connor, (2)

Please don't delete (parts of) the template; see the guidelines for the why.

2. Relevant equations
you need some equations here for this kind of motion. What do you have ?

3. The attempt at a solution
So far you have decomposed the ball velocity in horizontal and vertical component. Looks good.
Now what ?

And: did you make a drawing ?

3. Sep 11, 2016

### connor67

i have made a drawing but i am confused on the next step.

4. Sep 12, 2016

### BvU

You want to build up an expression for the distance thrown, in terms of 'known' variables: an expression in symbols, preferably with $t$ eliminated. A condition for maximum distance is that the derivative of that expression wrt e.g. $\theta$ is zero.