The accompanying graph represents the theoretical relationship between the volume and the temperature of a gas under constant pr
essure. image According to this graph, the volume of the gas is (5 points) Select one: a. directly proportional to the square of the temperature b. directly proportional to the temperature c. inversely proportional to the temperature d. inversely proportional to the square of the temperature
2 answers:
<u>Answer:</u> The correct answer is Option b.
<u>Explanation:</u>
Direct relationship is defined as the relationship in which if one variable increases, the other also increases and vice-versa.
where, 'x' and 'y' are two variables.
Indirect relationship is defined as the relationship in which if one variable increases, the other variable decreases and vice-versa.
where, 'x' and 'y' are two variables.
In the question, the two variables are Temperature and Volume and to determine the proportionality of the two variables, we will look at the slope of the graph.
If the slope of the graph is positive, then these variables follow direct proportionality and if the slope is negative, then these variables follow inverse proportionality.
Slope of the graph is calculated by using the formula:
As, the slope is positive, so the volume and temperature follow direct proportionality.
Hence, the correct answer is Option b.
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Answer:
The ball will drop 0.881 m by the time it reaches the catcher.
Explanation:
The position of the ball at time "t" is described by the position vector "r":
r = (x0 + v0x · t, y0 + v0y · t + 1/2 · g · t²)
Where:
x0 = initial horizontal position.
v0x = initial horizontal velocity.
t = time.
y0 = initial vertical position.
v0y = initial vertical velocity.
g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).
When the ball reaches the catcher, the position vector will be "r final" (see attached figure).
The x-component of the vector "r final", "rx final", will be 17.0 m. We have to find the y-component.
Using the equation of the x-component of the position vector, we can calculate the time it takes the ball to reach the catcher (notice that the frame of reference is located at the throwing point so that x0 and y0 = 0):
x = x0 + v0x · t
17.0 m = 0 m + 40.1 m/s · t
t = 17.0 m/ 40. 1 m/s = 0.424 s
With this time, we can calculate the y-component of the vector "r final", the drop of the ball:
y = y0 + v0y · t + 1/2 · g · t²
Initially, there is no vertical velocity, then, v0y = 0.
y = 1/2 · g · t²
y = -1/2 · 9.8 m/s² · (0.424 s)²
y = -0.881 m
The ball will drop 0.881 m by the time it reaches the catcher.
