A person throws a baseball from height of 7 feet with an initial vertical velocity of 50 feet per second. Use the vertical motio
2 answers:
Answer:
3.25 seconds
Explanation:
It is given that,
A person throws a baseball from height of 7 feet with an initial vertical velocity of 50 feet per second. The equation for his motion is as follows :
Where
s is the height in feet
For the given condition, the equation becomes:
When it hits the ground, h = 0
i.e.
It is a quadratic equation, we find the value of t,
t = 3.25 seconds and t = -0.134 s
Neglecting negative value
Hence, for 3.25 seconds the baseball is in the air before it hits the ground.
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Answer:
v = 7934.2 m/s
Explanation:
Here the total energy of the Asteroid and the Earth system will remains conserved
So we will have
now we know that
now from above formula
now we have
now plug in all data
This question is incomplete, the complete question;
you make an interferometer using 50-50 beam splitter and two mirrors, one being a perfect mirror and one which does not reflect all light. The wavelength of the 9 mW incident laser is 400 nm.
Because the top mirror is not perfectly reflective (it reflects 90% of the photons, allowing 10% of them to go through), the power measured at the detector when only the vertical arm is blocked is 2.25 mW, while the power measured at the detector when only the horizontal arm is blocked is only 2.025 mW. Assume initially the intensity is at its maximum. How much would we need to translate the perfect mirror to the right to get a minimum intensity at detector, and what is that minimum intensity
Options;
a) 200 nm; 0.9 mW
b) 100 nm, 0.0059 mW
c) 200 nm; 0 mW
d) 100 nm; 0.9 mW
e) 200 nm; 0.0059 mW
Answer:
the amount we need to translate the perfect mirror to the right to get a minimum intensity at detector and the minimum intensity are;
100 nm; 0.0059 mW
Option b) 100 nm, 0.0059 mW is the correct answer
Explanation:
Given that the instrument here is an interferometer.
Maximum intensity is obtained when the two waves are exactly in phase.
that is the peaks (crusts and troughs) and nodes (zero value points) of the two waves will be at the exact same point when the wave falls on the detector.
The phase factor of this point is taken as ∅ = 0
Now, to get a minimum point, the phase difference between the two waves should be should be ∅ = π
This corresponds to a path difference between the two waves as half of the wavelength. λ/2
The light gets reflected from the mirror.
Hence, when we move the mirror by a length l, the extra/less path the light has to travel is 2l (light is going and coming back)
hence, to get a path difference of λ/2 the mirror should move half of this distance only
so, the mirror should move;
= λ/4
here, wavelength is 400nm
the length moved by the mirror = 400/4 = 100 nm
The intensity is given by the equation;
=
1 +
2 + 2√
1
2cos(∅)
where
1 = 2.25 mW
2 = 2.025 mW
∅ = π
so we substitute
= 2.25 + 2.025 - 2√(2.25 × 2.025)
= 4.275 - 4.26907
= 0.0059
Therefore; the amount we need to translate the perfect mirror to the right to get a minimum intensity at detector and the minimum intensity are;
100 nm; 0.0059 mW
Option b) 100 nm, 0.0059 mW is the correct answer
The velocity of the current in a river has no effect on the the time it takes to paddle a canoe across the river, given that the boat is pointed perpendicular to the bank of the river, because
The velocity of the river does not change the velocity and therefore the distance traveled in the direction of the boat which is directed perpendicular to it
Reason:
Let represent the velocity of the boat across the river in the direction,
, and let,
, represent the velocity of the river, we have;
The velocity of the boat perpendicular to the direction of the river =
Therefore, the distance covered per unit time in the perpendicular direction
to the flow of the river is , such that the time it takes to cross the river in
the perpendicular direction is the same, for every value of the velocity of
the river.
This is so because the velocity in the perpendicular direction to the flow of
the river, which is the velocity of the boat is unchanged by the velocity of
the river, because there is no perpendicular component of velocity in the
velocity of the river.
= 3 m/s
= 4 m/s
The width of the river, = 6 meters, we have;
- The resultant velocity =
The direction, θ, is given as follows;
The length of the path of the boat, <em>l</em>, is given as follows;
The length of the path the boat takes = 10 m
The time it takes to cross the river, t = , therefore;
- The time it takes to cross the river, t = 2 seconds
Considering only the y-components, we have;
Therefore;
Which expresses that the time taken is the same and given that the
vectors of the velocities of the river and the boat are perpendicular, the
distance covered in the direction of the boat is unaffected by the velocity
of the river.
Learn more vectors here: