Answer:
9 cm
-36 cm
Explanation:
u = Object distance
v = Image distance
f = Focal length = 12
m = Magnification = 4
![m=-\frac{v}{u}\\\Rightarrow 4=-\frac{v}{u}\\\Rightarrow v=-4u](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7Bv%7D%7Bu%7D%5C%5C%5CRightarrow%204%3D-%5Cfrac%7Bv%7D%7Bu%7D%5C%5C%5CRightarrow%20v%3D-4u)
Lens equation
![\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\\\Rightarrow \frac{1}{12}=\frac{1}{u}+\frac{1}{-4u}\\\Rightarrow \frac{1}{12}=\frac{3}{4u}\\\Rightarrow u=9\ cm](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bf%7D%3D%5Cfrac%7B1%7D%7Bu%7D%2B%5Cfrac%7B1%7D%7Bv%7D%5C%5C%5CRightarrow%20%5Cfrac%7B1%7D%7B12%7D%3D%5Cfrac%7B1%7D%7Bu%7D%2B%5Cfrac%7B1%7D%7B-4u%7D%5C%5C%5CRightarrow%20%5Cfrac%7B1%7D%7B12%7D%3D%5Cfrac%7B3%7D%7B4u%7D%5C%5C%5CRightarrow%20u%3D9%5C%20cm)
Object distance is 9 cm
![v=-4\times 9=-36\ cm](https://tex.z-dn.net/?f=v%3D-4%5Ctimes%209%3D-36%5C%20cm)
Image distance is -36 cm (other side of object)
Answer:
510448 Joules
102089.6 J
13.61194 min
Explanation:
![1\ kcal=4184\ J](https://tex.z-dn.net/?f=1%5C%20kcal%3D4184%5C%20J)
![122\ cal=122\times 4184=510448\ J](https://tex.z-dn.net/?f=122%5C%20cal%3D122%5Ctimes%204184%3D510448%5C%20J)
The energy in Joules is 510448 Joules.
20% of energy
![0.2\times 510448=102089.6\ J](https://tex.z-dn.net/?f=0.2%5Ctimes%20510448%3D102089.6%5C%20J)
The energy is 102089.6 J
Power is given by
![P=\dfrac{E}{t}\\\Rightarrow t=\dfrac{E}{P}\\\Rightarrow t=\dfrac{102089.6}{125}\\\Rightarrow t=816.7168\ s=\dfrac{816.7168}{60}=13.61194\ min](https://tex.z-dn.net/?f=P%3D%5Cdfrac%7BE%7D%7Bt%7D%5C%5C%5CRightarrow%20t%3D%5Cdfrac%7BE%7D%7BP%7D%5C%5C%5CRightarrow%20t%3D%5Cdfrac%7B102089.6%7D%7B125%7D%5C%5C%5CRightarrow%20t%3D816.7168%5C%20s%3D%5Cdfrac%7B816.7168%7D%7B60%7D%3D13.61194%5C%20min)
The number of minutes is 13.61194 min
An average person consumes around 2000-2500 kcal
![0.2\times 122=24.4\ kcal](https://tex.z-dn.net/?f=0.2%5Ctimes%20122%3D24.4%5C%20kcal)
This is done in 13.61194 min
In one hour
![\dfrac{24}{13}\times 60=110.76923\ kcal](https://tex.z-dn.net/?f=%5Cdfrac%7B24%7D%7B13%7D%5Ctimes%2060%3D110.76923%5C%20kcal)
So, it is easy to consume the calories.
Answer:
Explanation:
given,
mass of hoop = 2.75 Kg
horizontal speed = 4.5 m/s
angle with horizontal = 25°
m g l sin θ = m ( v² - u² )
g l sin θ = ( v² - u² )
9.8 x 3 x sin 25° = ( v² - 4.5² )
12.425 = v² - 20.25
v² = 32.675
v = 5.72 m/s
Rotational
![K E = \dfrac {1}{2}I\omega^2](https://tex.z-dn.net/?f=K%20E%20%3D%20%5Cdfrac%20%7B1%7D%7B2%7DI%5Comega%5E2)
The different seasons are mainly cause by a planet's tilt of it's axis.
In short, Your Answer would be Option C
Hope this helps!
Answer:
Explanation:
given,
speed of the pebble = 14 m/s
height of the building = 31 m
ignoring air resistance
a) horizontally
V_x = 14 m/s
time = ![\sqrt{\dfrac{2h}{g}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cdfrac%7B2h%7D%7Bg%7D%7D)
time = ![\sqrt{\dfrac{2\times 31}{9.8}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cdfrac%7B2%5Ctimes%2031%7D%7B9.8%7D%7D)
times = 2.52 s
v_y = 9.8 x 2.52
v_y = 24.7 m/s
resultant velocity
= ![\sqrt{24.7^2+14^2}](https://tex.z-dn.net/?f=%5Csqrt%7B24.7%5E2%2B14%5E2%7D)
= 28.39 m/s
b) vertically straight up
max height = ![\dfrac{v^2}{2g}](https://tex.z-dn.net/?f=%5Cdfrac%7Bv%5E2%7D%7B2g%7D)
= ![\dfrac{15^2}{2\times 9.8}](https://tex.z-dn.net/?f=%5Cdfrac%7B15%5E2%7D%7B2%5Ctimes%209.8%7D)
= 11.47 m
height covered = 31 + 11.47
= 42.47 m
velocity = ![\sqrt{2gh}](https://tex.z-dn.net/?f=%5Csqrt%7B2gh%7D)
= ![\sqrt{2\times 9.8 \times 42.47}](https://tex.z-dn.net/?f=%5Csqrt%7B2%5Ctimes%209.8%20%5Ctimes%2042.47%7D)
= 28.85 m/s
c) vertically down
v² = u² + 2as
v² = 2 × 9.8 × 31 +14²
v² = 803.6
v = 28.35 m/s