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2 answers:
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Answer:
12.5 ft/s
Explanation:
Height of person = 6 ft
height of lamp post = 10 ft
According to the question,
dx / dt = 5 ft/s
Let the rate of tip of the shadow moves away is dy/dt.
According to the diagram
10 / y = 6 / (y - x)
10 y - 10 x = 6 y
y = 2.5 x
Differentiate both sides with respect to t.
dy / dt = 2.5 dx / dt
dy / dt = 2.5 (5) = 12.5 ft /s
Answer:
The centripetal acceleration as a multiple of is
Explanation:
The centripetal acceleration is defined as:
(1)
Where v is the velocity and r is the radius
Since the person is standing in the Earth surfaces, their velocity will be the same of the Earth. That one can be determined by means of the orbital velocity:
(2)
Where r is the radius and T is the period.
For this case the person is standing at a latitude . Remember that the latitude is given from the equator. The configuration of this system is shown in the image below.
It is necessary to use the radius at the latitude given. That radius can be found by means of trigonometric.
(3)
Where is the radius at the latitude of
and
is the radius at the equator (
).
can be isolated from equation 3:
(4)
Then, equation 2 can be used
Notice that the period is the time that the Earth takes to give a complete revolution (24 hours), this period will be expressed in seconds for a better representation of the velocity.
⇒
Finally, equation 1 can be used:
Hence, the centripetal acceleration is
To given the centripetal acceleration as a multiple of it is gotten:
Answer:
E = 4.83 N/ C
Explanation:
If we have a uniform charge sphere we can use the following formulas to calculate the Electric field due to the charge of the sphere:
: Formula (1) To calculate the electric field in the region outside the sphere r ≥ a
Where:
K: coulomb constant (N*m²/C²)
a: sphere radius (m)
Q: Total sphere charge (C)
r : Distance from the center of the sphere to the region where the electric field is calculated (m)
Equivalences
1nC=10⁻⁹C
1cm= 10⁻²m
Data
k= 9*10⁹ N*m²/C²
Q=4nC=4 *10⁻⁹C
D = 26 cm = 26*10⁻²m = 0.26m
a = D/2 = 0.13m
r= R+a = 2.6 m+ 0.13m = 2.73m
Problem development
Magnitude of the electric field at r = 2.73m from the center of the sphere
r>a , We apply the Formula (1) :
E= 4.83 N/ C