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Answer:
What is the magnitude of the player 's displacement? A baseball "diamond" is a square, each side of length 27.4 m, with home plate and if each length of the base is 27.4 m, and the baseball player ran to third base,Then, the baseball player is 27.4 feet away from home plate (where he started)below the horizontal.
Explanation:
the sum of vectors we were able to find the displacement of the corridor for each case
a) d = 38.75 m
b) d = 27.4 m
c) d = 0 m
given parameters
- the distance of each side of the square r = 27.4m
to find
- the distance in three cases
A) a double
B) A triple
c) A home run
The displacement is a vector for which, in addition to the module, it has a direction, so it must be taken into account for the calculations. In the exercise, set a reference system with the x-axis in the direction from Home to first base and the y-axis from home to third base.
To find the displacement we use the Pythagoras theorem
d = [tex]\sqrt{d_x^2 + d_y^2}[/tex]
if the displacements are on a single axis the addition reduces to arithmetic addition
Let's analyze the different cases:
a) hit a double
runner goes from home plate to second base
d = [tex]\sqrt{r^2+r^2}[/tex]Ra r² + r²
d = r √2
d = 27.4 √2
d = 38.75 m
b) hit a triple
Runner goes from home plate to third base
the distance from home to first base x = r
the distance from second to third base x = -r
the negative sign indicates that it is going in the opposite direction
d = [tex]\sqrt{(r-r)^2 +r^2}[/tex]
d = r
c) Hit a home run
in this case, the runner returns to the starting point, because of a vector the displacement is zero
d = 0
In conclusion, applying the sum of vectors we were able to find the displacement of the corridor for each case
a) d = 38.75 m
b) d = 27.4 m
c) d = 0
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