Question

Please give a logical answer
-Thanks

Answer 1

Displacement is AC.
$ab = \sqrt{5} \: m \\ bc = 3 \: m \\ cd = 2 \: m \\ \\ using \: pythgoras \: theorem \: in \: triangle \: bcd \\ \\ {bd}^{2} = {bc}^{2} - {cd}^{2} \\ bd = \sqrt{{bc}^{2} - {cd}^{2}} \\ bd = \sqrt{ {3}^{2} - {2}^{2} } \\ bd = \sqrt{9 - 4} \\ bd = \sqrt{5} \: m$

$ad = ab + bd = \sqrt{5} + \sqrt{5} = 2 \sqrt{5} \: m$

$in \: triangle \: acd \\ \\ {ac}^{2} = {ad}^{2} + {dc}^{2} \\ ac = \sqrt{{ad}^{2} + {dc}^{2}} \\ ac = \sqrt{ {(2 \sqrt{5}) }^{2} + {(2)}^{2} } \\ ac = \sqrt{20 + 4} \\ ac = \sqrt{24} \\ ac = 2 \sqrt{6} \: m$

Displacement is AC = 2√6 m

Answer 2

AB =✓5 m
BC =3m
CD =2m

In ∆BCD, using Pythagoras theorem

${BC}^{2} = {CD}^{2} + {BD}^{2} \\ {3}^{2} = {2}^{2} + {BD}^{2} \\ {BD}^{2} = 9 - 4 \\ BD = \sqrt{5} m$
So AD = ✓5+✓5=2✓5
In ∆ACD, using Pythagoras theorem

${AC}^{2} = {CD}^{2} + {AD}^{2} \\ {AC}^{2} = {2}^{2} + {2✓5}^{2} \\ {AC}^{2} = 4+20\\ AC= \sqrt{24} m\\AC=2✓6m$