Answer:
a. Δx = 2.59 cm
Explanation:
mb = 0.454 kg , mp = 5.9 x 10 ⁻² kg , vp = 8.97 m / s , k = 21.0 N / m
Using momentum conserved
mb * (0) + mp * vp = ( mb + mp ) * vf
vf = ( mp / mp + mb) * vp
¹/₂ * ( mp + mb) * (mp / mp +mb) ² * vp ² = ¹/₂ * k * Δx²
Solve to Δx '
Δx = √ ( mp² * vp² ) / ( k * ( mp + mb )
Δx = √ ( ( 5.9 x 10⁻² kg ) ² * (8.97 m /s) ² / [ 21.0 N / m * ( 5.9 x10 ⁻² kg + 0.454 kg ) ]
Δx = 0.02599 m ⇒ 2.59 cm
Answer:

Explanation:
The equation for work is:

We can substitute the given values into the equation:

For a wave:
v = fλ
v is the velocity, f is the frequency, and λ is the wavelength.
Assuming the velocity of the wave doesn't change...
If you increase its frequency, its wavelength will shorten.
Answer:
Acceleration, 
Explanation:
Initial velocity of a particle in vector form, u = (-5i - 2j) m/s
Final velocity of particle in vector form, v = (-6i + 7j) m/s
Time taken, t = 8 seconds
We need to find the magnitude of acceleration vector. The changing of velocity w.r.t time is called acceleration of a particle. It is given by :

or

Hence, the value of acceleration vector is solved.