Related Rates Word Problem /Shadow of a Man

[StarlitxSunshine]

A man 6ft tall is walking towards a streetlight 18ft high at a rate of 3ft/second.

a). At what rate is his shadow length changing?

=>
s is the length of his shadow. p is the length from him to the lamp.

Using proportional triangles:
18s = 6s + 6p
18ds/dt= 6ds/dt + 6dp/dt

3ds/dt = ds/dt + dp/dt
2ds/dt = dp/dt

2ds/dt = 3

ds/dt = 3/2 ft/s

b). How fast is the tip of his shadow moving ?

I don't understand what they mean by the tip of his shadow. If the man is walking towards the right, is the very far left of his shadow ? And wouldn't it be moving at the same speed that the length is changing ?

 

[Deleted member 4993]

A man 6ft tall is walking towards a streetlight 18ft high at a rate of 3ft/second.

a). At what rate is his shadow length changing?

=>
s is the length of his shadow. p is the length from him to the lamp.

Using proportional triangles:
18s = 6s + 6p
18ds/dt= 6ds/dt + 6dp/dt

3ds/dt = ds/dt + dp/dt
2ds/dt = dp/dt

2ds/dt = 3

ds/dt = 3/2 ft/s

b). How fast is the tip of his shadow moving ?

I don't understand what they mean by the tip of his shadow. If the man is walking towards the right, is the very far left of his shadow ? And wouldn't it be moving at the same speed that the length is changing ?


The distance of tip of the shadow (from the lamp) = s+p

speed of tip = ds/dt + dp/dt