Consumed by Fire and Brimstone would be 1 symptom of Gomorrah lol
Answer:
A concave mirror has a radius of curvature of 20 cm. What is it's focal length? If an object is placed 15 cm in front of it, where would the image be formed? What is it's magnification?
The focal length is of 10 cm, object distance is 30 cm and magnification is -2.
Explanation:
Given:
A concave mirror:
Radius of curvature of the mirror, as C = 20 cm
Object distance in-front of the mirror = 15 cm
a.
Focal length:
Focal length is half of the radius of curvature.
Focal length of the mirror =
= 10 cm
According to the sign convention we will put the mirror on (0,0) point, of the Cartesian coordinate open towards the negative x-axis.
Object and the focal length are also on the negative x-axis where focal length and image distance will be negative numerically.
b.
We have to find the object distance:
Formula to be use:
⇒ 
⇒ Plugging the values.
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
Image will be formed towards negative x-axis 30 cm away from the pole.
c.
Magnification (m) is the negative ratio of mage distance and object distance:
⇒ 
⇒ 
⇒ 
The focal length of the concave mirror, is of 10 cm, object distance is 30 cm and magnification is -2.
With 30degree because incident angle = reflected angle
Answer: 
The ball was thrown at the speed of
.
Maximum height achieved is 
Time of flight is t.
Now, the time the ball takes to achieve maximum height = the time taken by ball to fall back = 
let us just consider the second half of the flight. At
, the velocity would be zero. let us consider as the initial velocity for the second half of the flight i.e. 
Using the equation of motion:

where,
is the final velocity, a is the acceleration, t is the time taken.
Because the ball would fall under gravity, hence a=g and time of flight would be t/2

Answer:
a) when the length of the rope is doubled and the angular frequency remains constant: The power increases by factor of two
b) when the amplitude is doubled and the angular frequency is halved: The power is the same
c) when both the wavelength and the amplitude are doubled: The power increases by a factor of 8
d) when both the length of the rope and the wavelength are halved: The power increases by factor of two
Explanation:
For a sinusoidal mechanical wave (Transverse wave), the time-averaged power is the energy associated with a wavelength divided by the period of the wave.

where;
A is the Amplitude
ω is the angular frequency
λ is the wavelength
a) when the length of the rope is doubled and the angular frequency remains constant
L = λ/2, λ = 2L
The power increases by factor of two
b) when the amplitude is doubled and the angular frequency is halved

The power is the same
c) when both the wavelength and the amplitude are doubled

The power increases by a factor of 8
d) when both the length of the rope and the wavelength are halved
L = λ/2
when both are halved
L/2 = λ/4, λ = 2L
The power increases by factor of two