A boy walks 10 m due west and 10m due south.What is the displacement.[2]a girl walks 12m northwards,5m eastwards and 7m southwards.Calculate her total displacement[3]a man walks 5km south and 3km in the direction 60 degree west of south.Calculate his distance from starting point.
2. Disp. = 12i + 5 - 7i = 5 + 5i = 7.07m[45o].
3. All angles are measured CW from +y-axis.
Disp. = 5[180o] + 3[240o].
X = 5*sin180 + 3*sin240 = -2.60 km.
Y = 5*Cos180 + 3*Cos240 = -6.5 km.
Disp. = -2.60 + (-6.5)I = 7.0[22o] W. of S. = 7.0km[202o] CW.
Using Pythagoras theorem the answer is 14.1 for question 1
To find the displacement, we need to calculate the straight-line distance and direction from the starting point to the final position.
[1] For the boy who walks 10 m due west and 10 m due south:
We can represent this visually with a coordinate system. The initial position is at (0, 0). Walking 10 m due west means moving to (-10, 0), and then walking 10 m due south brings us to (-10, -10). Now, we can calculate the straight-line distance using the Pythagorean theorem:
Displacement = √((-10)^2 + (-10)^2) = √(100 + 100) = √200 ≈ 14.14 m
[2] For the girl who walks 12 m northwards, 5 m eastwards, and 7 m southwards:
Again, let's use a coordinate system with the initial position at (0, 0). Walking 12 m northwards brings us to (0, 12). Then, moving 5 m eastwards takes us to (5, 12), and finally, walking 7 m southwards brings us to (5, 5). Now, we can find the straight-line distance:
Displacement = √((5 - 0)^2 + (5 - 0)^2) = √(25 + 25) = √50 ≈ 7.07 m
[3] For the man who walks 5 km south and 3 km in the direction 60 degrees west of south:
To calculate the distance from the starting point, we need to break down the motion into its horizontal and vertical components. Walking 5 km south means moving in the negative y-direction by 5 km. Then, walking 3 km in the direction 60 degrees west of south can be represented as moving in the x- and y-directions, where deltaX = 3 km * cos(60°) and deltaY = 3 km * sin(60°):
deltaX = 3 km * cos(60°) = 3 km * 0.5 = 1.5 km
deltaY = 3 km * sin(60°) = 3 km * √(3)/2 ≈ 2.6 km
Now, we can find the displacement using the Pythagorean theorem:
Displacement = √(deltaX^2 + deltaY^2) = √(1.5^2 + 2.6^2) ≈ 3.03 km
Therefore, the man is approximately 3.03 km away from his starting point.
these all just use the Pythagorean Theorem, or the distance formula, which is the same.
Just figure out the final location, and then use the formula.
For #1,
(0,0) -> (-10,0) -> (-10,-10)
distance is √(10^2+10^2) = 14.1