Question

The mosquito net over a 7m x 4m bed is 3m high. The net has a hole at one corner of the bed through which a mosquito enters the net. It flies and sits at the diagonally opposite upper corner of the net. (a)Find the magnitude of the displacement of the mosquito.
(b)Taking the hole as horizon, the length of the bed as X-axis, its width as Y-axis and vertically up as the Z-axis, write the components of the displacement vector

Answer 1

Here hole is at the corner H

(a) The magnitude of displacement of mosquito is given by

$HA=\sqrt{l^2+b^2+c^2}$

$HA=\sqrt{7^2+4^2+3^2}$

$HA=\sqrt{49+16+9}$

$HA=\sqrt{74}cm$

(b) Clealy from the diagram the coordinates of point A is (-7,3,-4).

So displacement vector is given by

$\overrightarrow{HA}=-7\hat{i}+3\hat{k}-4\hat{k}$

Hence components of displacement vector are 7ft,3ft and 4ft respectively