2(A + B)
1 answer:
Answer:
θ = cos^(-1) (-A/B)
Explanation:
The image of the reauktant forces A & B are missing, so i have attached it.
Now, from the attached image, we will see that;
Angle between A and B is θ
Also;
A = Bcos(180° − θ)
Now, in trigonometry, we know that;
cos(180° − θ) = -cosθ
Thus;
A = -Bcosθ
cosθ = -A/B
Thus;
θ = cos^(-1) (-A/B)
You might be interested in
Answer:
a) t= 0.92 s
b) h = 0.46 m
c) v = -6.04 m/s
Explanation:
A)
- In order to find the total time that the feet are in the air, we must add two times:
- 1) time needed to reach to the maximum height (t₁)
- 2) time from when starts to fall from the maximum height until her feet hit the water (t₂)
- In order to get t₁, we need to take into account that at her highest point, the vertical speed will be zero.
- Taking for granted the value for the acceleration due to gravity,
- g = -9.8 m/s2, we can apply the definition of acceleration, and replacing by the givens, we can find t₁ as follows:
- In order to find t₂, we need to find first the highest point above the board, which is indeed what is asked for in b).
- We can use the following kinematic equation, taking into account that at the highest point, the final velocity vf will be zero.
- The equation can be written as follows:
- Replacing by the givens, and solving for Δh, we get:
- The total height over the water will be just the sum of the takeoff point (1.40 m over the water) and the value we found in (3):
- H = 1.40 m + 0.46 m = 1.86 m
- Now, we can use the equation that relates the vertical displacement with the time, remembering that v₀=0, as follows:
- Replacing by the givens and the value found for H in (4), and solving for t, we get the value of t₂, as follows:
- The total time will the sum of t₁ and t₂:
- t = 0.3 s + 0.62 s = 0.92 s (6)
B)
- As we have just found, the highest point above the board was at 0.46m above the takeoff point, so the highest point above the board is just 0.46 m.
C)
- In order to find the velocity when her feet hit the water, we can use the same equation (2), taking into account that v₀=0, and Δh = H= -1.86m.
- Solving (2) for vf, we get:
Answer:
Velocity of electron along x direction is 57.9 m/s
Explanation:
The uncertainty in x coordinate of electron, Δx = 0.200 mm = 0.2 x 10⁻³ m
Let vₓ be the x component of electrons velocity.
The uncertainty in x component of electrons momentum is:
Δpₓ = mΔvₓ
Here m is mass of the electron.
The uncertainty in velocity x component is 1% i.e. 0.01.
So, the above equation can be written as :
Δpₓ = 0.01mvₓ ....(1)
The minimum uncertainty principle is:
....(2)
Here h is Planck's constant.
From equation (1) and (2),
Substitute 0.2 x 10⁻³ m for Δx, 9.1 x 10⁻³¹ kg for m and 6.626 x 10⁻³⁴ m²kg/s in the above equation.
vₓ = 57.9 m/s