Question

A street light is at the top of a 10 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole?

Answer 1

the shadow is moving with 12ft/s from the woman

Step-by-step explanation:

let the distance from the pole to the shadow tip be L

`(10)/(6) = (L)/(x)`

`L=(5)/(3)x`

`\frac{\mathrm{d} (QR)}{\mathrm{d} t}= 8ft/s`

`\frac{\mathrm{d} (L-x)}{\mathrm{d} t}= 8ft/s`

`\frac{\mathrm{d} (L)}{\mathrm{d} t}-\frac{\mathrm{d} (x)}{\mathrm{d} t}= 8ft/s`

`\frac{\mathrm{d} (L)}{\mathrm{d} t}=(5)/(3)\frac{\mathrm{d} (x)}{\mathrm{d} t}`

`\frac{\mathrm{d} (x)}{\mathrm{d} t}=12ft/s`

`\frac{\mathrm{d} (L)}{\mathrm{d} t}=16ft/s`

hence the shadow is moving with 12ft/s from the woman