v1f = -0.16 ms
Explanation:
Use the conservation law of linear momentum:
m1v1i + m2v2i = m1v1f + m2v2f
where
v1i = v2i = 0
m1 = 160 kg
m2 = 0.50 kg
v2f = 50m/s
v1f = ?
So we have
0 = (160 kg)v1f + (0.5 kg)(50 m/s)
v1f = -(25 kg-m/s)/(160 kg)
= -0.16 m/s
Note: the negative sign means that its direction is opposite that of the arrow.
Answer:
Time period, 
Explanation:
Given that,
The quartz crystal used in an electric watch vibrates with a frequency of 32,768 Hz, f = 32768 Hz
We need to find the period of the crystal's motion. The relationship between the frequency and the time period is given by :

T is the time period of the crystal's motion.
Time period is given by :

So, the time period of the crystal's motion is
. Hence, this is the required solution.
Answer:
Increase in total energy will be equal to the increase in the internal energy i.e
Joules
Explanation:
Given
Weight of sledge hammer
kilogram
Speed of sledge hammer
meter per second
Kinetic energy is equal to half the product of mass and velocity square

Substituting the value of mass and velocity, we get -

It is given that one fourth of the energy is converted into internal energy
One fourth of kinetic energy is equal to

Increase in total energy will be equal to the increase in the internal energy i.e
Joules
Velocity can be calculated using the following rule:
velocity = lambda * frequency where:
velocity is given = 6 km/sec
lambda is the wavelength that we want to calculate
frequency is given = 13 Hz
Substitute with the givens in the above equation to get the wavelength (lambda) as follows:
6 = 13*lambda
wavelength = 6/13 = 0.461538 Km = 461.538 meters
Answer
given,
Length of the string, L = 2 m
speed of the wave , v = 50 m/s
string is stretched between two string
For the waves the nodes must be between the strings
the wavelength is given by

where n is the number of antinodes; n = 1,2,3,...
the frequency expression is given by

now, wavelength calculation
n = 1

λ₁ = 4 m
n = 2

λ₂ = 2 m
n =3

λ₃ = 1.333 m
now, frequency calculation
n = 1


f₁ = 12.5 Hz
n = 2


f₂= 25 Hz
n = 3


f₃ = 37.5 Hz