Rates of Change Question (1 Viewer)

[Shuuya]

Question:

A man 1.5m tall is walking directly towards a street lamp 8 metres off the ground at a speed of 36km/h.

(i) Find the rate at which the length of his shadow is decreasing.
(ii) Find the speed with which the tip of his shadow is moving along the path.

Thanks!

 

[integral95]

Question:

A man 1.5m tall is walking directly towards a street lamp 8 metres off the ground at a speed of 36km/h.

(i) Find the rate at which the length of his shadow is decreasing.
(ii) Find the speed with which the tip of his shadow is moving along the path.

Thanks!

You sure there's no diagram or anything?

 

[Shuuya]

You sure there's no diagram or anything?

Nope, that's why I'm finding it hard to visualise...

 

[Squar3root]

I think it is something like this

 

[Paradoxica]

Question:

A man 1.5m tall is walking directly towards a street lamp 8 metres off the ground at a speed of 36km/h.

(i) Find the rate at which the length of his shadow is decreasing.
(ii) Find the speed with which the tip of his shadow is moving along the path.

Thanks!

Let x be the distance between the man and the street lamp, s be the length of his shadow, and S be the sum of these two distances.

Will be using metres per second

dx/dt = 10ms^-1

Now the man and his shadow form a triangle similar to the street lamp and the distance from the tip of his shadow to the base of the street lamp.

So, we thus have

height of man / shadow = height of street lamp / base to shadow tip length

1.5/s = 8/S

3S = 16s

Note that S = x+s

3x = 13s

3dx/dt = 13ds/dt

30ms^-1 = 13ds/dt

ds/dt = 30/13 ms^-1

that which is the rate at which his shadow length decreases.

And as for the second part, you are simply finding dS/dt, which is trivial in comparison to the first part.

Now, the real question is:

Who walks at 10 metres per second?

That is already a world record level sprinting speed.

 

[eyeseeyou]

@Shuuya

Do you think you could do my rates of change question?