A student travels 4.0m East, 8.0m South, 4.0m west, and finally 8.0m north. What is her displacement
1 answer:
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Answer:
(a):
(b):
(c):
(d):
(e):
Explanation:
Given, the position of the particle along the x axis is
The units of terms and
should also be same as that of x, i.e., meters.
The unit of t is seconds.
(a):
Unit of
Therefore, unit of
(b):
Unit of
Therefore, unit of
(c):
The velocity v and the position x of a particle are related as
(d):
The acceleration a and the velocity v of the particle is related as
(e):
The particle attains maximum x at, let's say, , when the following two conditions are fulfilled:
Applying both these conditions,
For ,
Since, c is a positive constant therefore, for ,
Thus, particle does not reach its maximum value at
For ,
Here,
Thus, the particle reach its maximum x value at time
Answer:
The volume of water displaced by the raft is 0.233 m³
Explanation:
The question relates to Archimedes' principle which states that the buoyant force experienced by an object immersed in a fluid is equal to the weight of (the force of gravity on) the displaced fluid
The given parameters are;
The combined mass of the person and the raft, m = 233 kg
The liquid on which the raft is located = Water
The density of water, = 1000 kg/m³
Weight = Mass, m × g
Where;
m = The mass of the object
g = The acceleration due to gravity = 9.8 m/s²
Given that the raft is on the surface of the water (floating), the buoyant force is equal to the combined weight of the person and the raft = 233 kg
The combined weight of the person and the raft, = 233 kg × 9.8 m/s² = 2,283.4 N
Therefore;
The buoyant force = 2,283.4 N = The weight of the water displaced
The mass of the water displaced, , = 2,283.4 N/(9.8 m/s²) = 233 kg
Density = Mass/Volume
The volume of water displaced by the raft = The mass of the water displaced/(The density of the water) = 233 kg/(1,000 kg/m³) = 0.233 m³.
Answer:
The gravitational force is related to the mass of each object.
The gravitational force is an attractive force.
Explanation:
Gravitational force is a long range force of attraction between any two masses.
Mathematically given as :
where:
are the masses
r= distance between the center of mass of the two objects.
G= gravitational constant =
From the above relation of eq. (1) it is clear that,
Gravitational force is inversely proportional to the square of the distance and directly proportional to the masses.
The mass of an object is independent of its size due to the fact that density may vary for different objects.
The force of gravity varies with height as:
where:
gravity at height
of the center of mass of the object from the center of mass of the earth.
and we know that force:
where: m= mass of the object.