Dante is leading a parade across the main street in front of city hall. Starting at city hall, he marches the parade 4 blocks ea
st, then 3 blocks south. From there, the parade marches 1 block west and 9 blocks north and finally stops. What is the vector displacement and direction of the the parade, starting from the city hall and the stopping point? (1 point)
2 answers:
Answer:
The displacement between the city hall and the stopping point is 6.7 blocks.
The direction is 63.43°
Explanation:
The diagram explains better.
From the diagram, point O is the city hall and point D is the stopping point.
The displacement between O and D is OD.
Using Pythagoras theorem, we can find this:
OD² = OX² + DX²
From the diagram:
OX = 4 - 1 = 3 blocks
DX = 9 - 3 = 6 blocks
=> OD² = 3² + 6² = 9 + 36
OD² = 45
=> OD = 6.7 blocks
To get the direction, θ, we use SOHCAHTOA:
tanθ = DX/OX
tanθ = 6/3 = 2
=> θ = 63.43°
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Answer:
The shortest de Broglie wavelength for the electrons that are produced as photoelectrons is 0.81 nm
Explanation:
Given;
wavelength of ultraviolet light, λ = 270 nm
work function of the metal, φ = 2.3 eV = 2.3 x 1.602 x 10⁻¹⁹ J = 3.685 x 10⁻¹⁹ J
The energy of the ultraviolet light is given by;
The energy of the incident light is related to kinetic energy of the electron and work function of the metal by the following equation;
E = φ + K.E
K.E = E - φ
K.E = (7.362 x 10⁻¹⁹ J) - (3.685 x 10⁻¹⁹ J )
K.E = 3.677 x 10⁻¹⁹ J
K.E = ¹/₂mv²
mv² = 2K.E
velocity of the electron is given by;
the shortest de Broglie wavelength for the electrons is given by;
Therefore, the shortest de Broglie wavelength for the electrons that are produced as photoelectrons is 0.81 nm