Answer:
Explanation:
Work is defined as the scalar product of force and distance 
W=F•d
Given that
 F = 8.5i + -8.5j. +×-=-
F=8.5i-8.5j
 d = 2.5i + cj
If the work in the practice is zero, then W=0
therefore,
W=F•ds
0=F•ds
0=(8.5i -8.5j)•(2.5i + cj)
Note that 
i.i=j.j=k.k=1
i.j=j.i=k.i=i.k=j.k=k.j=0
So applying this
0=(8.5i -8.5j)•(2.5i + cj)
0= (8.5×2.5i.i + 8.5×ci.j -8.5×2.5j.i-8.5×cj.j)
0=21.25-8.5c
Therefore,
8.5c=21.25
c=21.25/8.5
c=2.5
 
        
             
        
        
        
Answer:

Explanation:
let  be the mass attached, let
 be the mass attached, let  be the spring constant and let
 be the spring constant and let  be the positive damping constant.
 be the positive damping constant.
-By Newton's second law:

where  is the displacement from equilibrium position. The equation can be transformed into:
 is the displacement from equilibrium position. The equation can be transformed into:
 shich is the equation of motion.
  shich is the equation of motion.
 
        
             
        
        
        
Answer:
The effective spring constant of the firing mechanism is 1808N/m.
Explanation:
First, we can use kinematics to obtain the initial velocity of the performer. Since we know the angle at which he was launched, the horizontal distance and the time in which it's traveled, we can calculate the speed by:

(This is correct because the horizontal motion has acceleration zero). Then:

Now, we can use energy to obtain the spring constant of the firing mechanism. By the conservation of mechanical energy, considering the instant in which the elastic band is at its maximum stretch as t=0, and the instant in which the performer flies free of the bands as final time, we have:

Then, plugging in the given values, we obtain:

Finally, the effective spring constant of the firing mechanism is 1808N/m.
 
        
             
        
        
        
Answer:
a)  v = 2,9992 10⁸ m / s
, b)  Eo = 375 V / m
,  B = 1.25 10⁻⁶ T,
 c)     λ = 3,157 10⁻⁷ m,   f = 9.50 10¹⁴ Hz
,  T = 1.05 10⁻¹⁵ s
, UV
Explanation:
In this problem they give us the equation of the traveling wave
         E = 375 cos [1.99 10⁷ x + 5.97 10¹⁵ t]
a) what the wave velocity
all waves must meet
         v = λ f
In this case, because of an electromagnetic wave, the speed must be the speed of light.
         k = 2π / λ
         λ = 2π / k
         λ = 2π / 1.99 10⁷
         λ = 3,157 10⁻⁷ m
         w = 2π f
         f = w / 2 π
         f = 5.97 10¹⁵ / 2π
         f = 9.50 10¹⁴ Hz
the wave speed is
         v = 3,157 10⁻⁷   9.50 10¹⁴
         v = 2,9992 10⁸ m / s
b) The electric field is
            Eo = 375 V / m
to find the magnetic field we use
            E / B = c
            B = E / c
             B = 375 / 2,9992 10⁸
             B = 1.25 10⁻⁶ T
c) The period is
            T = 1 / f
             T = 1 / 9.50 10¹⁴
             T = 1.05 10⁻¹⁵ s
the wavelength value is
           λ = 3,157 10-7 m (109 nm / 1m) = 315.7 nm
this wavelength corresponds to the ultraviolet