The equatorial radius of the earth is
r = 6378 km = 6378 x 10³ m
The earth makes 1 revolution in 24 hours.
The angular velocity is
ω = (2π rad)/(24*3600 s) = 7.2722 x 10⁻⁵ rad/s
The tangential velocity (linear velocity) at a point on the equator is
v = rω
= (6378 x 10³ m)*(7.2722 x 10⁻⁵ rad/s)
= 463.8 m/s
Answer: 463.8 m/s
Answer:

Explanation:
The standard form of the 2nd order differential equation governing the motion of mass-spring system is given by

Where m is the mass, ζ is the damping constant, and k is the spring constant.
The spring constant k can be found by




The damping constant can be found by



Finally, the mass m can be found by



Where g is approximately 32 ft/s²

Therefore, the required differential equation is


The initial position is

The initial velocity is

We/Wm = ge/gm = 120N/1.2N
or
gm = ge/100 = 0.1 m/s^2
density = mass/volume = 3M/(4pir^3)
Re-arranging this equation, we get
M/r^2 = (4/3)×pi×(density)×r
From Newton's universal law of gravitation, the acceleration due to gravity on the moon gm is
gm = G(M/r^2) = G×(4/3)×pi×(density)×r
Solving for density, we get the expression
density = 3gm/(4×pi×G×r)
= 3(0.1)/(4×3.14×6.67×10^-11×2.74×10^6)
= 130.6 kg/m^3
Explanation:
It is given that,
Speed of the baseball, u = 44 m/s
Speed of the baseball, v = 53 m/s
Mass of the ball, m = 145 g = 0.145 kg
Time of contact between the ball and the bat, t = 2.2 ms = 0.0022 s



F₁ = 2900 N...........(1)



F₂ = 3493.18 N.........(2)
In average vector form force is given by :



Hence, this is the required solution.
Complete Question
One day, after pulling down your window shade, you notice that sunlight is passing through a pinhole in the shade and making a small patch of light on the far wall. Having recently studied optics in your physics class, you're not too surprised to see that the patch of light seems to be a circular diffraction pattern. It appears that the central maximum is about 2 cm across, and you estimate that the distance from the window shade to the wall is about 5 m.
Required:
Estimate the diameter of the pinhole.
Answer:
The diameter is 
Explanation:
From the question we are told that
The central maxima is 
The distance from the window shade is 
The average wavelength of the sun is mathematically evaluated as

Generally the visible light spectrum has a wavelength range between 400 nm to 700 nm
So the initial wavelength of the sun is 
and the final wavelength is 
Substituting this into the above equation


The diameter is evaluated as

substituting values

