Students in a physics lab applied several mathematical models to determine where a ball projected horizontally off a table will land. Their resulting equation for determining where the ball will land (R) is given in the box below. Note that in the equation the term vx represents the horizontal velocity of the ball as it leaves the table, h is the height of the table, and g is the acceleration due to gravity.R = the v_x root of (2h / g)What type of relationship between height of table (h) and range (R) is represented in this equation? Choose the best statement below.a. A negative correlation exists between range (R) and height of table (h).b. No correlation exists between the range (R) and height of table (h).c. A causal relationship exists between the range (R) and height of table (h).d. A causal relationship exists between the range (R) and height of table (h) if the horizontal velocity (vx) and acceleration due to gravity is held constant.e. Both c and d.
The type of relationship between the height of the table (h) and the range (R) represented in the given equation is e
The type of relationship between the height of the table (h) and the range (R) represented in the given equation is e. Both c and d.
Explanation:
c. A causal relationship exists between the range (R) and height of the table (h):
The equation provided allows us to determine the range (R) of a ball projected horizontally off a table based on the height of the table (h). This implies that the height of the table causally affects the range of the ball. As the height of the table increases or decreases, the range of the ball will also change accordingly.
d. A causal relationship exists between the range (R) and height of the table (h) if the horizontal velocity (vx) and acceleration due to gravity are held constant:
In addition to the relationship described in (c), this option accounts for the important condition that the horizontal velocity (vx) and the acceleration due to gravity remain constant. If these conditions are met, the only factor influencing the range (R) of the ball will be the height of the table (h), as indicated by the given equation.
Therefore, the correct answer is e. Both c and d.
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