Answer:
50 kg
Explanation:
f=ma
Force = mass x acceleration
490 = 9.8 x m
m = 50 kg
Igneous rocks are rocks that form through the cooling and solidification of magma or lava.
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)
Answer:
32 pounds
Explanation:
The amount of water in the 200 pound person is
200 * 60% = 200*0.6 = 120 pounds
Of the 120 pounds, a third of this is extracellular fluid, the amount of extracellular fluid is
120 / 3 = 40 pounds
20 % of this is in the blood, which amounts to
40 * 20% = 40 * 0.2 = 8 pounds
The rest is interstitial fluid, which is
40 - 8 = 32 pounds
Explanation:
Given that,
Mass of the cart, ![m_1=1\ kg](https://tex.z-dn.net/?f=m_1%3D1%5C%20kg)
Mass of the cart 2,
Final speed of cart 2, ![v_2=0.3\ m/s](https://tex.z-dn.net/?f=v_2%3D0.3%5C%20m%2Fs)
Final speed of cart 1 is 0 as it comes to rest.
Let us assume that the initial velocity of the cart 2 is 0. So using the conservation of linear momentum as :
![m_1u_1+m_2u_2=m_1v_1+m_2v_2\\\\m_1u_1+0=0+m_2v_2\\\\m_1u_1=m_2v_2\\\\u_1=\dfrac{m_2v_2}{m_1}\\\\u_1=\dfrac{3\times 0.3}{1}\\\\u_1=0.9\ m/s](https://tex.z-dn.net/?f=m_1u_1%2Bm_2u_2%3Dm_1v_1%2Bm_2v_2%5C%5C%5C%5Cm_1u_1%2B0%3D0%2Bm_2v_2%5C%5C%5C%5Cm_1u_1%3Dm_2v_2%5C%5C%5C%5Cu_1%3D%5Cdfrac%7Bm_2v_2%7D%7Bm_1%7D%5C%5C%5C%5Cu_1%3D%5Cdfrac%7B3%5Ctimes%200.3%7D%7B1%7D%5C%5C%5C%5Cu_1%3D0.9%5C%20m%2Fs)
So, the initial velocity of the 1.0-kg cart is 0.9 m/s.