need help on calc

[Xylitol]

A ball is thrown from the origin of a coordinate systme. The equation of its path is y = mx - (e^(2m))/1000 * x^2, where m is positive and represents the slope of the path at the origin.

a) For what value of m will the ball strike the horizontal axis at the greatest distance from the origin? Justify your answer.

I just don't know how to solve this problem since I can't isolate the X in order to optimize it and find the maximum value of it. Is there something that I'm missing?

Thanks

edit: got m = 1/2
sounds right - anyone wanta double check?

 

[GML3G0]

At the maximum distance, y=0. So the y disappears and you have an equation x(m) that you can optimize.

 

[Xylitol]

Originally posted by: GML3G0
At the maximum distance, y=0. So the y disappears and you have an equation x(m) that you can optimize.

yea but you still can't separate out the x

 

[GML3G0]

Yes you can. mx - ( (x^2) * e^(2m) )/ 1000 = 0.

Get x in terms of m. x = 1000m/(e^2m) Differentiate that and set it equal to 0.

 

[blinky8225]

Well, it's a parabola, and upside down one at that. What you want to do is differentiate it, and you can find the max in terms of m. Since it starts at the origin, and parabolas are symmetrical, simply double the x value of the max to find where it hits 0, again. That x value will be in terms of m. You can find the max of the that x value in the same way you found the max of the parabola.

 

[Xylitol]

got it thanks guys
i got m=1/2

anyone wanta check my answer?

 

[TridenT]

Originally posted by: Xylitol
got it thanks guys
i got m=1/2

anyone wanta check my answer?

Nope, I do not check answers of people who say wanta.

 

[GodlessAstronomer]

Originally posted by: TridenTBoy3555

Originally posted by: Xylitol
got it thanks guys
i got m=1/2

anyone wanta check my answer?

Nope, I do not check answers of people who say wanta.

Stop being a douche.

I got 1/sqrt(2) but I haven't done this stuff in a while so could be wrong.

Edit - I just checked again, 1/2 is correct.

 

[Cheesetogo]

Originally posted by: TridenTBoy3555

Originally posted by: Xylitol
got it thanks guys
i got m=1/2

anyone wanta check my answer?

Nope, I do not check answers of people who say wanta.

Somebody ban this guy already...

Edit: From a physics standpoint, 45 degrees will give you the most horizontal distance with a projectile, so there's some further reinforcement for your answer.

 

[blinky8225]

Originally posted by: Xylitol
got it thanks guys
i got m=1/2

anyone wanta check my answer?

I got the same thing; you're good to go.