Answer:
false dots just false I dont how to explain it false
Complete question:
The length of nylon rope from which a mountain climber is suspended has an effective force constant of 1.40 ×10⁴ N/m.
What is the frequency (in Hz) at which he bounces, given that his mass plus the mass of his equipment is 84.0 kg?
Answer:
The frequency (in Hz) at which he bounce is 2.054 Hz
Explanation:
Given;
effective force constant, K = 1.40 ×10⁴ N/m.
The total mass = his mass plus the mass of his equipment, m = 84 kg
The frequency (in Hz) at which he bounce is given by;
![f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}\\\\f = \frac{1}{2\pi} \sqrt{\frac{1.4*10^4}{84}}\\\\f = 2.054 \ Hz](https://tex.z-dn.net/?f=f%20%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%7D%20%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%7D%5C%5C%5C%5Cf%20%3D%20%20%5Cfrac%7B1%7D%7B2%5Cpi%7D%20%5Csqrt%7B%5Cfrac%7B1.4%2A10%5E4%7D%7B84%7D%7D%5C%5C%5C%5Cf%20%3D%202.054%20%5C%20Hz)
Therefore, the frequency (in Hz) at which he bounce is 2.054 Hz
Answer:
<em>The average speed is 22.2 km/h</em>
Explanation:
<u>Average Speed</u>
Given an object travels a total distance d and took a total time t, then the average speed is:
![\displaystyle \bar v=\frac{d}{t}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbar%20v%3D%5Cfrac%7Bd%7D%7Bt%7D)
The mailman first drives d1=7 km at v1=15 km/h. The time taken to drive is:
![\displaystyle t1=\frac{d1}{v1}=\frac{7}{15}=0.467\ h](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t1%3D%5Cfrac%7Bd1%7D%7Bv1%7D%3D%5Cfrac%7B7%7D%7B15%7D%3D0.467%5C%20h)
Then he drives d2=7 km at v2=43 km/h taking a time of:
![\displaystyle t2=\frac{d2}{v2}=\frac{7}{43}=0.163\ h](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t2%3D%5Cfrac%7Bd2%7D%7Bv2%7D%3D%5Cfrac%7B7%7D%7B43%7D%3D0.163%5C%20h)
The total time is
t=0.467 h + 0.163 h = 0.63 h
The total distance is
d = 7 km + 7 km = 14 km
The average speed is:
![\displaystyle \bar v=\frac{14}{0.63}=22.2\ km/h](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbar%20v%3D%5Cfrac%7B14%7D%7B0.63%7D%3D22.2%5C%20km%2Fh)
The average speed is 22.2 km/h
Answer:
The mass of the cart is 150 kg.
Explanation:
Given that,
Mass of a boy, m₁ = 50 kg
Initial speed of boy, u₁ = 10 m/s
Initial speed of car, u₂ = 0 (at rest)
The speed of the cart with the boy on it is 2.50 m/s, V = 2.5 m/s
Let m₂ is the mass of the cart. Using the conservation of momentum as follows :
![m_1u_1+m_2u_2=(m_1+m_2)V\\\\50(10)+m_2(0)=(50+m_2)(2.5)\\\\500=125+2.5m_2\\\\375=2.5m_2\\\\m_2=150\ kg](https://tex.z-dn.net/?f=m_1u_1%2Bm_2u_2%3D%28m_1%2Bm_2%29V%5C%5C%5C%5C50%2810%29%2Bm_2%280%29%3D%2850%2Bm_2%29%282.5%29%5C%5C%5C%5C500%3D125%2B2.5m_2%5C%5C%5C%5C375%3D2.5m_2%5C%5C%5C%5Cm_2%3D150%5C%20kg)
So, the mass of the cart is 150 kg.