Answer:
v₂ = 176.24 m/s
Explanation:
given,
angle of projectile = 45°
speed = v₁ = 150 m/s
for second trail
speed = v₂ = ?
angle of projectile = 37°
maximum height attained formula,
![H_{max}= \dfrac{v^2 sin^2(\theta)}{g}](https://tex.z-dn.net/?f=H_%7Bmax%7D%3D%20%5Cdfrac%7Bv%5E2%20sin%5E2%28%5Ctheta%29%7D%7Bg%7D)
now,
![H_{max}= \dfrac{v_1^2 sin^2(\theta_1)}{g}](https://tex.z-dn.net/?f=H_%7Bmax%7D%3D%20%5Cdfrac%7Bv_1%5E2%20sin%5E2%28%5Ctheta_1%29%7D%7Bg%7D)
![H_{max}= \dfrac{v_2^2 sin^2(\theta_2)}{g}](https://tex.z-dn.net/?f=H_%7Bmax%7D%3D%20%5Cdfrac%7Bv_2%5E2%20sin%5E2%28%5Ctheta_2%29%7D%7Bg%7D)
now, equating both the equations
![\dfrac{v_2^2}{v_1^2}=\dfrac{sin^2(\theta_1)}{sin^2(\theta_2)}](https://tex.z-dn.net/?f=%5Cdfrac%7Bv_2%5E2%7D%7Bv_1%5E2%7D%3D%5Cdfrac%7Bsin%5E2%28%5Ctheta_1%29%7D%7Bsin%5E2%28%5Ctheta_2%29%7D)
![\dfrac{v_2^2}{150^2}=\dfrac{sin^2(45^0)}{sin^2(37^0)}](https://tex.z-dn.net/?f=%5Cdfrac%7Bv_2%5E2%7D%7B150%5E2%7D%3D%5Cdfrac%7Bsin%5E2%2845%5E0%29%7D%7Bsin%5E2%2837%5E0%29%7D)
v₂² = 31061.79
v₂ = 176.24 m/s
velocity of projectile would be equal to v₂ = 176.24 m/s
Answer:
d = 1.55 * 10⁻⁶ m
Explanation:
To calculate the distance between the adjacent grooves of the CD, use the formula,
..........(1)
The fringe number, m = 1 since it is a first order maximum
The wavelength of the green laser pointer,
= 532 nm = 532 * 10⁻⁹ m
Distance between the central maximum and the first order maximum = 1.1 m
Distance between the screen and the CD = 3 m
= Angle between the incident light and the diffracted light
From the setup shown in the attachment, it is a right angled triangle in which
![sin(A_{m}) = \frac{opposite}{Hypotenuse} \\sin(A_{m}) =\frac{1.1}{\sqrt{1.1^{2}+3^{2}}}](https://tex.z-dn.net/?f=sin%28A_%7Bm%7D%29%20%3D%20%5Cfrac%7Bopposite%7D%7BHypotenuse%7D%20%5C%5Csin%28A_%7Bm%7D%29%20%3D%5Cfrac%7B1.1%7D%7B%5Csqrt%7B1.1%5E%7B2%7D%2B3%5E%7B2%7D%7D%7D)
![sin(A_{m} ) = 0.344\\A_{m} = sin^{-1} 0.344\\A_{m} = 20.14^{0}](https://tex.z-dn.net/?f=sin%28A_%7Bm%7D%20%29%20%3D%200.344%5C%5CA_%7Bm%7D%20%3D%20sin%5E%7B-1%7D%200.344%5C%5CA_%7Bm%7D%20%3D%2020.14%5E%7B0%7D)
Putting all appropriate values into equation (1)
![d = \frac{1* 532*10^{-9} }{0.344 }\\d = 0.00000155 m\\d = 1.55 * 10^{-6} m](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7B1%2A%20532%2A10%5E%7B-9%7D%20%7D%7B0.344%20%7D%5C%5Cd%20%3D%200.00000155%20m%5C%5Cd%20%3D%201.55%20%2A%2010%5E%7B-6%7D%20m)
Answer:
Speed of the speeder will be 28 m/sec
Explanation:
In first case police car is traveling with a speed of 90 km/hr
We can change 90 km/hr in m/sec
So ![90km/hr=\frac{90\times 1000m}{3600sec}=25m/sec](https://tex.z-dn.net/?f=90km%2Fhr%3D%5Cfrac%7B90%5Ctimes%201000m%7D%7B3600sec%7D%3D25m%2Fsec)
Car is traveling for 1 sec with a constant speed so distance traveled in 1 sec = 25×1 = 25 m
After that car is accelerating with
for 7 sec
So distance traveled by car in these 7 sec
![S=ut+\frac{1}{2}at^2=25\times 7+\frac{1}{2}\times 2\times 7^2=224m](https://tex.z-dn.net/?f=S%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2%3D25%5Ctimes%207%2B%5Cfrac%7B1%7D%7B2%7D%5Ctimes%202%5Ctimes%207%5E2%3D224m)
So total distance traveled by police car = 224 m
This distance is also same for speeder
Now let speeder is moving with constant velocity v
so ![224=\left ( 1+7 \right )v](https://tex.z-dn.net/?f=224%3D%5Cleft%20%28%201%2B7%20%5Cright%20%29v)
v = 28 m/sec
In ur explanation make sure to use the terms
500 N is the answer, you just tell that the moon is attracted towards the person because of the Earth's huge mass.