Answer:
True.
Explanation:
The given statement is true that the law of universal gravitation offers a mathematical explanation for the attraction between the moon and Earth.
According to this law, the forces between two masses can be calculated by the product of their masses and divided by the square of the distance between them. Mathematically, it can be written as :

G is universal gravitational constant
Hence, the given statement is true.
Answer:
Vf = 210 [m/s]
Av = 105 [m/s]
y = 2205 [m]
Explanation:
To solve this problem we must use the following formula of kinematics.

where:
Vf = final velocity [m/s]
Vo = initial velocity = 0 (released from the rest)
g = gravity acceleration = 10 [m/s²]
t = time = 21 [s]
Vf = 0 + (10*21)
Vf = 210 [m/s]
Note: The positive sign for the gravity acceleration means that the object is falling in the same direction of the gravity acceleration (downwards)
The average speed is defined as the sum of the final speed plus the initial speed divided by two. (the initial velocity is zero)
Av = (210 + 0)/2
Av = 105 [m/s]
To calculate the distance we must use the following equation of kinematics

44100 = 20*y
y = 2205 [m]
M1 v1 = (m1 + m2)v2.
All of the exponents should be lowered to the bottom right of the letters.
Answer:
a) 2575 kgm²/s
b) 1.23 kJ
c) 0.478 rad/s
Explanation:
Given
Mass of astronauts, m = 74 kg
Length of rope, l = 8.53 m
Speed of orbit, v = 4.08 m/s
L = m1v1.x1(i) + m2v2.x2(i) = 2mv(d/2)
Thus, L = 2.m.v.(d/2)
L = 2 * 74 * 4.08 * (8.53/2)
L = 2 * 74 * 4.08 * 4.265
L = 2575.38 kgm²/s
Rotational Energy of the system
K(i) = 1/2m1v1(i)² + 1/2m2v2(i)²
K(i) = 2(1/2) * 74 * 4.08²
K(i) = 74 * 16.6464
K(i) = 1231.83 J = 1.23 kJ
Angular momentum is conserved, thus, angular velocity, w = v/r
w = 4.08 / 8.53
w = 0.478 rad/s
Answer: A. The total displacement divided by the time and C. The slope of the ant's displacement vs. time graph.
Explanation:
Hi! The question seems incomplete, but I found the options on the internt:
A. The total displacement divided by the time.
B. The slope of the ant's acceleration vs. time graph.
C. The slope of the ant's displacement vs. time graph.
D. The average acceleration divided by the time.
Now, since we know the ant is travelling at a constant speed, its average velocity
will be expressed by the following equation:

Where:
is the ant's total displacement
is the time it took to the ant to travel to the kitchen
Hence one of the correct options is: A. The total displacement divided by the time
On the other hand, this can be expressed by a displacement vs. time graph graph, where the slope of that line leads to the equation written above. So, the other correct option is:
C. The slope of the ant's displacement vs. time graph.