Initially, the velocity vector is 
. At the same height, the x-value of the vector will be the same, and the y-value will be opposite (assuming no air resistance). Assuming perfect reflection off the ground, the velocity vector is the same. After 0.2 seconds at 9.8 seconds, the y-value has decreased by 
, so the velocity is 
.
Converting back to direction and magnitude, we get 
Answer:
(a) A = 0.0800 m, λ = 20.9 m, f = 11.9 Hz
(b) 250 m/s
(c) 1250 N
(d) Positive x-direction
(e) 6.00 m/s
(f) 0.0365 m
Explanation:
(a) The standard form of the wave is:
y = A cos ((2πf) t ± (2π/λ) x)
where A is the amplitude, f is the frequency, and λ is the wavelength.
If the x term has a positive coefficient, the wave moves to the left.
If the x term has a negative coefficient, the wave moves to the right.
Therefore:
A = 0.0800 m
2π/λ = 0.300 m⁻¹
λ = 20.9 m
2πf = 75.0 rad/s
f = 11.9 Hz
(b) Velocity is wavelength times frequency.
v = λf
v = (20.9 m) (11.9 Hz)
v = 250 m/s
(c) The tension is:
T = v²ρ
where ρ is the mass per unit length.
T = (250 m/s)² (0.0200 kg/m)
T = 1250 N
(d) The x term has a negative coefficient, so the wave moves to the right (positive x-direction).
(e) The maximum transverse speed is Aω.
(0.0800 m) (75.0 rad/s)
6.00 m/s
(f) Plug in the values and find y.
y = (0.0800 m) cos((75.0 rad/s) (2.00 s) − (0.300 m⁻¹) (1.00 m))
y = 0.0365 m
The correct answer is 1.25 because it is 1/2 of 1 1/2 and that is 1.25.
I am a competitive figure skater. There are certain turns you can use such as a mowhawk, where you set one foot down that is facing the opposite direction from which you are gliding. There is a two foot turn, where you either go on or toes and turn backwards, or lean somewhat on your heals and turn forwards. Use your hips to help turn. And a 3 turn, which is basically a 2 foot turn on 1 foot. But remember, it takes practice, and you may fall a couple times.
Mechanics is dealing with forces that are effecting some body, electrostatics is about electrical fields of not moving bodies, and quantum mechanics is dealing with quantum states of atoms.
Thermodynamics as the word say, is dealing with thermal energy that is moving (transferring from one body to another or even better from one medium to another).
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