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anonymous
 one year ago
I can't think of how to label my illustration for this question... I need someone to direct me in the right way.
A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward first base with a speed of 26 ft/s.
At what rate is his distance from second base changing when he is halfway to first base?
anonymous
 one year ago
I can't think of how to label my illustration for this question... I need someone to direct me in the right way. A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward first base with a speed of 26 ft/s. At what rate is his distance from second base changing when he is halfway to first base?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1434166696015:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I've misplaced #1 and 3 but it shouldn't make a difference

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 thank god you're here! Can you help me on this?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4dw:1434167956990:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Mhmm and how do I label the info given in the question

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4dw:1434168228668:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.4apply pythagorean theorem, differentiate and do the usual stuff

wolf1728
 one year ago
Best ResponseYou've already chosen the best response.1Just to make things easier, most people visualize a baseball diamond with home plate at the bottom, 1st base on the left, etc.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So is this what I have to do... \[90^2+(90x)^2=y^2\] \[2(90x)=2yy'\] \[y'=\frac{ 2(90x) }{ 2y }\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2hint: using the drawing of @ganeshie8 we can write: \[y = \sqrt {{{90}^2} + {x^2}} \] furthermore, please keep in mind that: \[x = x\left( t \right) = vt = 26t\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wouldn't it be \[y=\sqrt{90^2+(90x)^2}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2the right triangle is: dw:1434170152802:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2when I write: \[y\left( t \right) = \sqrt {{{90}^2} + x{{\left( t \right)}^2}} \] am I right?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2dw:1434170615708:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok, now try to differentiate y(t) with respect to the time t, what do you get?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2please keep in mind that you have to use the chain rule, since: \[x = x\left( t \right) = vt = 26t\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Just a quick question, why is it x(t) on one of the legs?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2it is the distance between the current position of the player, from the first base

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2dw:1434170805543:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok! Now what is: \[\frac{{dy}}{{dt}} = y' = ...\]?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is it \[y'=\frac{ 1 }{ 2 }\sqrt{(x(t))^2 + 90^2} \times2x(t)x'(t)\] ??

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2use this rule: \[y = \sqrt x , \Rightarrow y' = \frac{1}{{2\sqrt x }}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 2x(t)x'(t) }{ 2\sqrt{x(t)^2+90^2} }\] like that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Relief! haha ok now what?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2now, as I wrote before, we have: \[x = x\left( t \right) = vt = 26t\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2so, what is: \[x' = \frac{{dx}}{{dt}} = ...?\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2next, we have to substitute the expression of x and its derivative, into the above firtst derivative of y(t)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait so why is x(t) = vt ? Is that coming from > distance = velocity * time

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2yes! I think that in your exercise, it is supposed that the motion of the player is an uniform motion

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohh gotcha! So we first find y' and then x' and then substitute x' into the equation we got from y'... am i following?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alrighty! So then \[y'=\frac{ 52x(t) }{ 2\sqrt{x(t)^2 +90^2} }\] right?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok! Now simplify: 52/2=26 and substitute x= vt

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohh so \[y'=\frac{ 26(26t) }{ \sqrt{(26t)^2+90^2} }\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2next we have to compute the time at which the player is at midpoint between the first base and the home plate

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2in other words we have to solve this equation: \[45 = 26t\] what is t?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0or should i leave it as a fraction 45/26 ?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2finally, replace t with 1.73 into your last formula for y' (t), and you will get your answer

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2better is the fraction form

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right cuz then I can cancel things out and at the end i get 25/90

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2please wait I'm checking your computation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh wait i made a mistake

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 25(45) }{ \sqrt{45^2 +90^2} }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ahhh awesome!! I really bugged you didn't I?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2It is all right! :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks so much!! I have one more question about this problem xD

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok! I can help you!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh my goodness I love you so much! :D It's also asking to find at what rate the player's distance from third base is changing at the same moment... would I have to start all over?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2yes! I think so!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2it is necessary, since we have to rewrite the function y(t), after that the procedure is the same as before

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1434173455402:dw is this drawing right?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2if we pick as origin of our xaxis the first base, then we have: dw:1434173776450:dw so: \[y\left( t \right) = \sqrt {{{90}^2} + {{\left\{ {90  x\left( t \right)} \right\}}^2}} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohhh so now I get what's happening!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's gonna be the only difference correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Otherwise I just do the same thing as before

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2yes! the procedure is the same as before, only the function y(t) is different

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I honestly don't know how to thank you!! You're a lifesaver! Many thanks!
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