a body displaced 12m due to east then 5m due to north then 9m vertically upward what is the resultant displacement?
sqrt (12^2 + 5^2) = sqrt(144+25) = 13
sqrt (13^2 + 9^2) = (sqrt(169+81) = sqrt(250) = 5 sqrt(10)
or: sqrt(12^2 + 5^2 + 9^2) = sqrt 250
since all three displacements are mutually perpendicular
(Same answer as damon)
Pizz give me correct answer
To find the resultant displacement, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the three displacements (east, north, and upward) as the three sides of a right-angled triangle.
Step 1: Draw a diagram to represent the displacements.
Let's draw a 2D diagram with an x-axis (east-west) and a y-axis (north-south). We start our displacement from the origin (0,0).
Step 2: Determine the x-component and y-component of the resultant.
The x-component of the total displacement is the sum of the eastward and westward displacements. In this case, there is only an eastward displacement of 12m, so the x-component is 12m.
The y-component of the total displacement is the sum of the northward and southward displacements. In this case, there is only a northward displacement of 5m, so the y-component is 5m.
Step 3: Calculate the resultant displacement using the Pythagorean theorem.
The square of the hypotenuse (resultant displacement) is equal to the sum of the squares of the two other sides (x-component squared + y-component squared):
resultant^2 = x-component^2 + y-component^2
resultant^2 = (12m)^2 + (5m)^2
resultant^2 = 144m^2 + 25m^2
resultant^2 = 169m^2
To find the resultant displacement, we take the square root of both sides:
resultant = sqrt(169m^2)
resultant = 13m
So, the resultant displacement is 13m.
Step 4: Determine the direction of the resultant displacement.
Since the x-component (eastward) is positive and the y-component (northward) is positive, the resultant displacement is in the northeast direction.
Thus, the resultant displacement is 13m in the northeast direction.