A person is going 40m north,30m east and then 30√2m southwest. the net displacement will be
Answers
Answer:
10m
Explanation:
Displacement is the shortest distance between two points. In this case, the starting and finish point.
You need not make it very complex, you can solve it using simple Pythagorean Theorem,
Sum of Square of Sides = Square of Hypotenuse
Simply draw a diagram of the path taken by the person.
We nee AD,
At C, he turned South West, so it would be 45 Degrees to the current path of Travel, And It would normally intersect AB at 45 Degrees.
Now in Triangle BCE
We know Angle C is 45, and Angle E is 45 as Angle B is 90 (180–90–45)
As Angles E and C are 45, that implies, sides CB and BE are also identical in length. 20 kms. And say Side CE = a
==> a^2 = 20^2 + 20^2
==> a = 20√2
As we know, CD = 30√2
==>ED = CD-CE = 30√2 - 20√2 = 10√2
Now in Triangle ADE, ED = 10√2 and AE = (30–20) = 10
And we know Angle A = 90
S0,
DE^2 = AE^2 + AD^2
==> (10√2)^2 = 10^2 + AD^2
==> AD = Sqrt(200–100) = 10 m
Good Luck