Construct c = a + b by drawing and calculating the direction and magnitude of c. The direction should be
1 answer:
the method of the coordinates we can find the vector sum of the two vectors given, therefore the answer is:
c = 10.15
a = 70.4º
measured counterclockwise from the positive side of the x-axis
given parameters
- vectors a and b
to find
- the vector adds
The sum of vectors must take into account finding both the magnitude of the vector that is a scalar and its direction.
One of the best methods to perform vector addition is to add their component and then find the resulting vector.
Let's use trigonometry to find the components of vectors a and b, we take the data from the diagram.
Vector a
magnitude m_a = 8.0
angle θ= 45º in the second quadrant
cos 45 = x_a / m_a
sin 45 = y_a / m_a
x_a = m_a cos 45
y_a = m_a sin 45
x_a = 8.0 cos 45 = 5.657
y_a = 8.0 sin 45 = 5.657
as we are in the second quadrant, see diagram
x_a = - 5,657
y_a = 5,627
Vactor b
magnitude m_b = 4.5
angle θ = 60º in the first quadrant
cos 60 = x_b / m_b
sin 60 = y_b / m_b
x_b = m_b cos 60
y_b = m_b sin 60
x_b = 4.5 cos 60 = 2.25
y_b = 4.5 sin 60 = 3.897
Having the components encode the components of the resulting vector
cₓ = x_a + x_b
c_y = y_a + y_b
cₓ = - 5.657 + 2.25 = 3.407
c_y = 5,657 + 3,897 = 9,554
With these values we can find the modulus of the vector using the Pythagoras Theorem
c =
c =
c = 10.14
for the angle we must use the trigonometry relations
tan θ =
θ = tan⁻¹
θ = tan⁻¹
θ = 70.4º
In conclusion with the method of coordinates we can find the resulting vector
magnitud c= 10.15
angle θ = 70.4º
measured counterclockwise from the positive side of the x axis
learn more about vector addition here:
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It is required an infinite work. The additional electron will never reach the origin.
In fact, assuming the additional electron is coming from the positive direction, as it approaches x=+1.00 m it will become closer and closer to the electron located at x=+1.00 m. However, the electrostatic force between the two electrons (which is repulsive) will become infinite when the second electron reaches x=+1.00 m, because the distance d between the two electrons is zero:
So, in order for the additional electron to cross this point, it is required an infinite amount of work, which is impossible.
In fact, assuming the additional electron is coming from the positive direction, as it approaches x=+1.00 m it will become closer and closer to the electron located at x=+1.00 m. However, the electrostatic force between the two electrons (which is repulsive) will become infinite when the second electron reaches x=+1.00 m, because the distance d between the two electrons is zero:
So, in order for the additional electron to cross this point, it is required an infinite amount of work, which is impossible.
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