Answer:
The position is
relative to the base of the ocean
Explanation:
From the question we are told that
The angle made by the incline with the horizontal is ![\theta = 24.0 ^o](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%2024.0%20%5Eo)
The constant acceleration is ![a = 3.82 \ m/s^2](https://tex.z-dn.net/?f=a%20%3D%20%203.82%20%5C%20m%2Fs%5E2)
The distance covered is ![d = 60.0 \ m](https://tex.z-dn.net/?f=d%20%3D%20%2060.0%20%5C%20m)
The height of the cliff is ![h = 50 .0 \ m](https://tex.z-dn.net/?f=h%20%20%3D%20%2050%20.0%20%5C%20m)
The velocity of the car is mathematically represented as
![v^2 = u^2 + 2ad](https://tex.z-dn.net/?f=v%5E2%20%3D%20u%5E2%20%2B%20%202ad)
The initial velocity of the car is u= 0
So
![v^2 = 2ad](https://tex.z-dn.net/?f=v%5E2%20%3D%20%202ad)
substituting values
![v^2 = 2 * 3.82 * 60](https://tex.z-dn.net/?f=v%5E2%20%3D%202%20%2A%20%203.82%20%2A%2060)
![v = 21.4 \ m/s](https://tex.z-dn.net/?f=v%20%3D%20%2021.4%20%5C%20m%2Fs)
The vertical component of this velocity is
![v_v = -v * sin(\theta )](https://tex.z-dn.net/?f=v_v%20%20%3D%20%20-v%20%2A%20sin%28%5Ctheta%20%29)
substituting values
![v_v = -21.4 * sin(24.0)](https://tex.z-dn.net/?f=v_v%20%20%3D%20-21.4%20%2A%20sin%2824.0%29)
![v_v = -8.7 \ m/s](https://tex.z-dn.net/?f=v_v%20%20%3D%20-8.7%20%5C%20m%2Fs)
The negative sign is because is moving in the negative direction of the y-axis
The horizontal component of this velocity is
![v_h = v * cos (\theta)](https://tex.z-dn.net/?f=v_h%20%20%3D%20%20v%20%2A%20cos%20%28%5Ctheta%29)
![v_h = 21.4 * cos (24.0)](https://tex.z-dn.net/?f=v_h%20%20%3D%20%2021.4%20%2A%20cos%20%2824.0%29)
![v_h = 19.5 \ m/s](https://tex.z-dn.net/?f=v_h%20%20%3D%2019.5%20%5C%20m%2Fs)
Now according to equation of motion we have
![h = v_v*t - \frac{1}{2} * g t^2](https://tex.z-dn.net/?f=h%20%20%3D%20%20v_v%2At%20%20-%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20%20g%20t%5E2)
substituting values
![50 = -8.7 t - \frac{1}{2} * 9.8 t^2](https://tex.z-dn.net/?f=50%20%20%3D%20%20-8.7%20t%20%20-%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20%209.8%20t%5E2)
using quadratic equation we have that
![t_1 = 2.42\ s \ and\ t_2 = -4.20\ s](https://tex.z-dn.net/?f=t_1%20%3D%202.42%5C%20s%20%5C%20and%5C%20%20%20t_2%20%3D%20%20-4.20%5C%20s)
given that time cannot be negative
![t = 2.42 \ s](https://tex.z-dn.net/?f=t%20%3D%202.42%20%5C%20s)
The car’s position relative to the base of the cliff when the car lands in the ocean is mathematically evaluate as
![P = v_h * t](https://tex.z-dn.net/?f=P%20%20%3D%20%20v_h%20%2A%20t)
substituting values
![P = 19.5 * 2.43](https://tex.z-dn.net/?f=P%20%20%3D%20%2019.5%20%2A%20%202.43)
![P = 47.4 \ m](https://tex.z-dn.net/?f=P%20%20%3D%20%2047.4%20%5C%20m)
Speed of particle B is 2v₀/3 m/s to the left. Particle A and particle B will always have equal speed since they experience equal forces.
<h3>Conservation of energy</h3>
The speed and direction of the particle B is determined by applying the principle of conservation of energy as follows;
K.E₁ + P.E₁ = K.E₂ + P.E₂
![\frac{1}{2} Mv^2_A + \frac{G}{r^2} = \frac{1}{2} Mv^2_B + \frac{G}{r^2} \\\\ \frac{1}{2} Mv^2_A = \frac{1}{2} Mv^2_B\\\\v^2_A = v^2_B\\\\v_A = v_B](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20Mv%5E2_A%20%2B%20%5Cfrac%7BG%7D%7Br%5E2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20Mv%5E2_B%20%2B%20%5Cfrac%7BG%7D%7Br%5E2%7D%20%5C%5C%5C%5C%20%5Cfrac%7B1%7D%7B2%7D%20Mv%5E2_A%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20Mv%5E2_B%5C%5C%5C%5Cv%5E2_A%20%3D%20v%5E2_B%5C%5C%5C%5Cv_A%20%3D%20v_B)
![v_B = \frac{2v_0}{3} \ m/s \ to \ the \ left](https://tex.z-dn.net/?f=v_B%20%3D%20%5Cfrac%7B2v_0%7D%7B3%7D%20%20%5C%20m%2Fs%20%5C%20to%20%5C%20the%20%5C%20left)
At any given position, the speed of particle A and particle B will be equal, since they experience equal force and they have equal masses.
The complete question is below:
Particle A and particle B, each of mass M, move along the x-axis exerting a force on each other. The potential energy of the system of two particles assosicated with the force is given by the equation U=G/r 2, where r is the distance between the two particles and G is a positive constant. At time t=T1 particle A is observed to be traveling with speed 2vo/3 to the left. The speed and direction of motion of particle B is ?
Learn more about conservation of energy here: brainly.com/question/166559
The average speed is 8 miles
Answer:
a
Explanation:
because it has compact molecules
Supernova observations.
Hope this helped, have a great day! :D