Question

6.a girl of high 90 cm is walking away from the base of a lamp - post at a speed of 1.2m/sec.if the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.

Answer 1

`1.6\; {\rm m}`.

Step-by-step explanation:

The distance between the girl and the lamp is
`(4\; {\rm s})\, (1.2\; {\rm m\cdot s^(-1)}) = 4.8\; {\rm m}`. Apply unit conversion and ensure that the height of the girl is in the same unit as other lengths:
`90\; {\rm cm} = 0.90\; {\rm m}`.

Let
`x` denote the length of the shadow, measured in meters.

Refer to the diagram attached (not to scale.) There are two right triangles in this scenario. The smaller right triangle consists of the girl (
`0.9`) and her shadow (
`x`), whereas the larger right triangle consists of the lamp (
`3.6`) and the segment between the top of the shadow of the girl and the base of the lamp (
`x + 4.8`).

These two right triangles are similar to one another because two of their angles are equal: the right angle, and the angle opposite to the girl. Therefore, the ratio between the sides of the two triangles would be equal:

`\displaystyle (x)/(x + 4.8) = (0.9)/(3.6)`.

Solve this equation for
`x`:

`x = 1.6` (unit: meters.)