If an equation is dimensionally correct, it does not mean that the equation must be true. On the other hand, when the equation is dimensionally correct, the equation cannot be true. Dimensional analysis is a technique used to check whether a relationship is correct
The acceleration due to gravity of the planet X is 1 m/s².
The given parameters;
- height above the ground, h = 100 m
- initial velocity of the rock, u = 15 m/s
- time of motion of the rock, t = 10 s
The acceleration due to gravity is calculated as follows;
Thus, the acceleration due to gravity of the planet X is 1 m/s²
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Answer:
A) R = (200 i ^ + 100 j ^ + 30k ^) m
, B) L = 223.61 m
, C) R = 225.61 m
Explanation:
Part A
This is a vector summing exercise, let's take a Reference System where the z axis corresponds to the height (flights), the x axis is the East - West and the y axis corresponds to the North - South.
Let's write the displacements
Descending from the apartment
10 flights of 3 m each, the total descent is 30 m
Z = 30 k ^ m
Offset at street level
L1 = 0.2 i ^ km
L2 = 0.1 j ^ km
Let's reduce everything to the SI system
L1 = 0.2 * 1000 = 200 i ^ m
L2 = 100 j ^ m
The distance traveled is
R = (200 i ^ + 100 j ^ + 30k ^) m
Part B
The horizontal distance traveled can be found with the Pythagorean theorem for the coordinates in the plane
L² = x² + y²
L = √ (200² + 100²)
L = 223.61 m
Part C
The magnitude of travel, let's use the Pythagorean theorem for the sum
R² = x² + y² + z²
R = √ (30² + 200² + 100²)
R = 225.61 m