Answer:
The gravitational acceleration on the planet is 5.00 m/s²
Explanation:
This situation resembles a free-fall scenario, but with a different gravitational constant; the provided equation is as follows:
y-yo = ½ gₐ t² (1)
They mention creating a squared time graph illustrating the distance variation, which is beneficial for linearizing a nonlinear curve - specifically, by plotting the axis raised to a power, in this case, the square against another variable.
Let's continue with the analysis, noting we have a linear relationship; we can write the line’s equation:
y1 = m x1 + b (2)
Here, “y1” is the dependent variable, “x1” is the independent variable, “m” is the slope, and “b” indicates the intercept
Since the stone is released with zero initial velocity, we observe that b = 0,
On the y-axis, we label time squared “t²”, and on the x-axis, we mark “y-yo.” For clarity, we can rewrite equation 1 as follows:
t² = 2 /gₐ (y-yo)
Aligning the two expressions allows us to relate the terms correspondingly
y1 = t²
x1 = (y-yo)
m = 2/gₐ
b= 0
After substituting, we find
m = 2/gₔ[/color=red.entries():count].
gₐ = 2/m
gₐ = 2/ 0.400
gₐ = 5.00 m/s²
Thus, the acceleration due to gravity measures at 5.00 m/s² on the planet, while being conscientious of significant figures
