Mechanics | Relativity Answers

hey i have a question on newton 3rd law . if every action has equal and opposite and equal reaction then when i rotate my hand in air the molecules of air should exert a equal force back to my hand and if the equal and opposite then my hand should not move through as an equal and opposite force opposing it.

A sinusoidal wave is described by y(x,t) = 3.0 sin (5.95t-4.20x)cm
where x is the position along the wave propagation. Determine the amplitude, wave
number, wavelength, frequency and velocity of the wave. (express in answer in meters not centimeter)

a boat entered a marina with an initial velocity of 2.58 m/s [W 25.0 N]. over an interval of 4.00 s the captain turned the boat towards a dock while they slowed the boat to a final velocity of 1.15 m/s. what was the average acceleration of the boat during the parking sequence?

If you throw a snowball straight upwards with a velocity of 19 m/s, what will the magnitude of its velocity be after 2.9 seconds?

If a sprinter starts from rest and reaches a speed of 3.3 m/s after 1.5s, how far did they travel is those 1.5s?

During a freeway safety review, you are studying a curve that is essentially 1/8 of a circle with a radius of 0.5 miles. The curve is banked so that the road makes an angle of 4 degrees to the horizontal throughout the curve. Your job is to begin the review by considering the worst-case scenario, a slick, ice-covered road, and finding the speed a standard passenger car (about 2000 lbs) must travel in order to maintain a horizontal path through the turn. The team you?re working with will use this information along with other data to determine the speed limit on this road

Giving the necessary mathematical expressions, discuss the transient and steady state
of a weakly damped forced oscillator. Show that the average power absorbed by a
forced oscillator is given by
<p > = (bF2/m) w2/w2-w2+4b2w2

A harmonic wave on a rope is described by
y(x,t)=(4.00 mm)sin[2pi/0.82m ((10m/s)t+x)]

i) Calculate the wavelength and time period of the wave. ii) Determine the
displacement and acceleration of the element of the rope located at x = 0.58 m at
time, t = 0.41 s.

An ambulance siren has frequency 250 Hz. The ambulance is headed towards an
accident site with a speed of 90 km/h. Two police officers on separate motor
cycles head for the same accident site: one follows the ambulance with a speed of
80 km/h and the other approaches the accident site from the other direction with a
speed of 80 km/h. What frequency does ambulance siren has for each of the police
officers? Take the speed of sound equal to 340 m/s.

The equation of motion of a damped harmonic oscillator is given by
d2x/dt2+2b dx/dt + w2x=0. m= 0.25 kg , b= 0.14/s and w = 18.4/s Calculate i) the time period; ii) number of oscillations in which its amplitude will become half of its initial value; and iii) number of oscillations in which its mechanical energy will reduce to half of its initial value.