Answer:
The magnetic field along x axis is

The magnetic field along y axis is zero.
The magnetic field along z axis is

Explanation:
Given that,
Length of the current element 
Current in y direction = 5.40 A
Point P located at 
The distance is


We need to calculate the magnetic field
Using Biot-savart law

Put the value into the formula

We need to calculate the value of 



Put the value into the formula of magnetic field


Hence, The magnetic field along x axis is

The magnetic field along y axis is zero.
The magnetic field along z axis is

We need to use the kinematic equation
S=ut+(1/2)at^2
where
S=displacement (+=up, in metres)
u=initial velocity (m/s)
t=time (seconds)
a=acceleration (+=up, in m/s^2)
Substitute values
S=displacement = 1.96-2.27 = -0.31 m (so that shot does not hit his head)
u=11.1
a=-9.81 (acceleration due to gravity)
-0.31=11.1t+(1/2)(-9.81)t^2
Rearrange and solve for t
-4.905t^2+11.1t-0.31=0
t=-0.02756 or t=2.291 seconds
Reject the negative root to give
t=2.29 seconds (to 3 significant figures)
** Missing info: Lines per mm = 500 **
Ans: The wavelength is = λ = 1414.21 nm
Explanation:
The formula for diffraction grading is:
dsinθ = mλ --- (1)
Where
d = 1/lines-per-meter = (1/500)*10^-3 = 2 * 10^-6
m = order = 1
λ = wavelength
θ = 45°
Plug in the values in (1):
(1) => 2*10^-6*sin(45°) = (1)λ
=> λ = 1414.21 nm
Temperature doesn't do anything, the boiling point of stuff decreases. If you put water in a vacuum chainber then it will start to boil
Answer:
A) 138.8g
B)73.97 cm/s
Explanation:
K = 15.5 Kn/m
A = 7 cm
N = 37 oscillations
tn = 20 seconds
A) In harmonic motion, we know that;
ω² = k/m and m = k/ω²
Also, angular frequency (ω) = 2π/T
Now, T is the time it takes to complete one oscillation.
So from the question, we can calculate T as;
T = 22/37.
Thus ;
ω = 2π/(22/37) = 10.5672
So,mass of ball (m) = k/ω² = 15.5/10.5672² = 0.1388kg or 138.8g
B) In simple harmonic motion, velocity is given as;
v(t) = vmax Sin (ωt + Φ)
It is from the derivative of;
v(t) = -Aω Sin (ωt + Φ)
So comparing the two equations of v(t), we can see that ;
vmax = Aω
Vmax = 7 x 10.5672 = 73.97 cm/s