The x-coordinates of two objects moving along the x-axis are given as a function of time (t).

x1= (4m/s)t
x2= -(161m) + (48m/s)t - (4 m/s^2)t^2

Calculate the magnitude of the distance of closest approach of the two objects. x1 and x2 never have the same value.

Question

The x-coordinates of two objects moving along the x-axis are given as a function of time (t).

x1= (4m/s)t
x2= -(161m) + (48m/s)t - (4 m/s^2)t^2

Calculate the magnitude of the distance of closest approach of the two objects. x1 and x2 never have the same value.

asnaseer · Answer

create an equation to represent the distance between the two x's. you can do this by finding x1-x2. lets call this 'y':$$y=x_1-x_2=4t-(-161+48t-4t^2)=4t+161-48t+4t^2$$$$y=4t^2-44t+161$$we want to minimize the value of y. this will happen when the first derivative of y is zero. so:$$y'=8t-44=0\implies t=\frac{44}{8}=\frac{11}{4}$$substitute this value for t into the equation for y to get the distance between them as follows:$$y_{min}=4(\frac{11}{4})^2-44(\frac{11}{4})+161=\frac{121}{4}-121+161=9.75m$$

anonymous · Answer

This is not the correct answer....

asnaseer · Answer

what do you think is the correct answer?

anonymous · Answer

Well I'm given an array of multiple choice answers...

asnaseer · Answer

which are?

anonymous · Answer

1. 39 m
2. 57 m
3. 43 m
4. 29 m
5. 35 m
6. 61 m
7. 27 m
8. 46 m
9. 34 m
10. 40 m

asnaseer · Answer

are you certain that you have stated the question correctly?

anonymous · Answer

The x-coordinates of two objects moving
along the x-axis are given as a function of
time t.
x1 = (4 m/s) t and
x2 = −(161 m) + (48 m/s) t − (4 m/s2) t2 .
Calculate the magnitude of the distance of
closest approach of the two objects. x1 and
x2 never have the same value.

asnaseer · Answer

then I cannot see where the mistake is - can you?

anonymous · Answer

The calculation doesnt seem to appear right in the last part. It equas over a hundred... that isnt correct either.

anonymous · Answer

equals*

anonymous · Answer

oh 11/2 is t

asnaseer · Answer

Oops - I added up incorrectly at the end, it should have been:$$y_{min}=4(\frac{11}{4})^2-44(\frac{11}{4})+161=\frac{121}{4}-121+161=70.25m$$but that doesn't match any of your answers either?

asnaseer · Answer

aha - yes - well spotted, so we get:$$y_{min}=4(\frac{11}{2})^2-44(\frac{11}{2})+161=\frac{121}{4}-121+161=40m$$

anonymous · Answer

yay.... crossing my fingers.

asnaseer · Answer

sorry about my silly mistakes :-(

anonymous · Answer

I should have actually looked and figured that out myself. But thank you. Do you think you could help me on this hot air balloon problem?

asnaseer · Answer

have you posted it on the left?

anonymous · Answer

yes.

asnaseer · Answer

ok - let me take a look