Find max distance of football thrown while running.

[connor67]

Homework Statement

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.

 

[BvU]

Hi Connor, (2)

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

Homework Equations

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

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 ?

 

[connor67]

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

 

[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.