Rate of Change Question (1 Viewer)

[Lukybear]

Simple calculus question that i just cannot get my brain around currently.

A lamp is 6m directly above a straight path. A man 2m tall walks along the path away from the light at a constant speed of 1 m/s. At what speed is the end of his shadow moving along the path? At what speed is the length of his shadow increasing.

 

[Shikobe]

i can't really draw the triangle on this but you can imagine a right angled triangle etc.

When the man has walked for t seconds, he is t metres away from the start(the position thats is directly under the lamp).
Now, if you draw a line that touches the mans head to the ground you get two similar triangles. Let x be the distance of the shadow on the ground.

So, 6/(t+x)=2/x, rearranging you get, x=t/2,
Therefore as t increases the shadows length increases by 1/2 metres.

Now, since we are find the speed at which the end of the shadow is increasing, you add up the distance the man and the shadow has traveled.
So, t+x=t+t/2=3t/2.
Sub. this value into the speed formula, s=d/t=(3t/2)/t=3/2m/s

 

[fullonoob]

bravo