C.Earth is the largest and most dense of the terrestrial planets
The reason is because the force due to the acceleration from gravity is constant. It's the same as the typical "dropping a bowling ball and feather (with no air resistance) at the same time". Gravity acts on all object with the same acceleration regardless of physical properties.
Question: How fast was the arrow moving before it joined the block?
Answer:
The arrow was moving at 15.9 m/s.
Explanation:
The law of conservation of energy says that the kinetic energy of the arrow must be converted into the potential energy of the block and arrow after it they join:
![\dfrac{1}{2}m_av^2 = (m_b+m_a)\Delta Hg](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7Dm_av%5E2%20%3D%20%28m_b%2Bm_a%29%5CDelta%20Hg)
where
is the mass of the arrow,
is the mass of the block,
of the change in height of the block after the collision, and
is the velocity of the arrow before it hit the block.
Solving for the velocity
, we get:
![$v = \sqrt{\frac{2(m_b+m_a)\Delta Hg}{m_a} } $](https://tex.z-dn.net/?f=%24v%20%3D%20%5Csqrt%7B%5Cfrac%7B2%28m_b%2Bm_a%29%5CDelta%20Hg%7D%7Bm_a%7D%20%7D%20%24)
and we put in the numerical values
,
![m_b = 1.40kg,](https://tex.z-dn.net/?f=m_b%20%3D%201.40kg%2C)
![\Delta H = 0.4m,](https://tex.z-dn.net/?f=%5CDelta%20H%20%3D%200.4m%2C)
![g= 9.8m/s^2](https://tex.z-dn.net/?f=g%3D%209.8m%2Fs%5E2)
and simplify to get:
![\boxed{ v= 15.9m/s}](https://tex.z-dn.net/?f=%5Cboxed%7B%20v%3D%2015.9m%2Fs%7D)
The arrow was moving at 15.9 m/s