Confirm Correctness of Ant's Shadow Movement Equation

[mit_hacker]

Homework Statement

(Q) A lamp is placed at the point (5,0) and it casts the shadow of an ant onto the y axis. When the ant is at point (1,2), how fast is the ant's shadow moving when the ant's x-coordinate is increasing at the rate of 1/2 units/sec and its y-coordinate is decreasing at 1/5units/sec?

I got -9/16. Is it correct? I just need to confirm whether I'm right or wrong.

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

That's not at all what I get. Too bad you didn't show your working- I might have been able to point out an error.

 

[mit_hacker]

Here we go!

Let the coordinates of the ant be x,y. Let the length of the shadow be s.

Our goal is to find ds/dt. By similar triangles, s/y = 5/(5-x).

So, 5s - sx = 5y
Differentiating,

5(ds/dt) - (s(dx/dt) + x(ds/dt)) = 5(dy/dt)

When (x,y) = (1,2), s = 5/2.

5(ds/dt) - (5/2)(1/2) - (1)(ds/st) = 5(-1/5).

4(ds/dt) = -9/4.

ds/st = -9/16

 

[HallsofIvy]

Let the coordinates of the ant be x,y. Let the length of the shadow be s.

Our goal is to find ds/dt. By similar triangles, s/y = 5/(5-x).

So, 5s - sx = 5y
Differentiating,

5(ds/dt) - (s(dx/dt) + x(ds/dt)) = 5(dy/dt)

When (x,y) = (1,2), s = 5/2.

5(ds/dt) - (5/2)(1/2) - (1)(ds/st) = 5(-1/5).

4(ds/dt) = -9/4.

You "lost a sign"
4(ds/dt)= +5/4- 1= 1/4, not -9/4.

ds/st = -9/16

 

[mit_hacker]

Dammit!

All because of this gross gross gross error, I got the answer wrong in the exam. How many marks do you think I'll lose (out of 5?).??

Thanks a ton!