Relative speed of Tina with respect to David is given by
now the acceleration of Tina with respect to David
now the relative displacement would be zero when Tina cross David
so now we have
now the speed of Tina at this moment is given as
<em>so the speed will be 52 m/s</em>
The maximum height is reached when the vertical component of the velocity is zero.
vertical direction:
acceleration: a = -g = -9.81m/s²
velocity: v = -g*t + v₀
position: y = -0.5*g*t² + v₀*t + y₀
For v= 0:
0 = -g*t + v₀ => t = v₀/g
Insert into position equation gives:
y(max) = (-0.5*v₀²/g) + (v₀²/g) + y₀ = (0.5*v₀²/g) + y₀
Given Information:
Initial speed of rock = vi = 30 m/s
escape speed of the asteroid = ve = 24 m/s
Required Information:
final speed of rock = vf = ?
Answer:
vf = 18 m/s
Explanation:
As we know from the conservation of energy
KEf + Uf = KEi + Ui
Where KE is the kinetic energy and U is the potential energy
0 + 0 = ½mve² - GMm/R
When escape speed is used, KEf is zero due to vf being zero. Uf is zero because the object is very far away from mass M, therefore, the equation becomes
GMm/R = ½mve²
m cancels out
GM/R = ½ve²
GM/R = ½(24)²
GM/R = 288
KEf + Uf = KEi + Ui
½mvi² + 0 = ½vf² - GMm/R
m cancels out
½vi² = ½vf² - GM/R
Substitute the values
½(30)² = ½vf² - (288)
½vf² = 450 - 288
vf² = 2(162)
vf = √324
vf = 18 m/s
Therefore, the final speed of the rock is 18 m/s
Nitrogen gas has a molar mass of about 28.0134 g/mol. Then we have a starting amount of
(42 g) / (28.0134 g/mol) ≈ 1.4993 mol
of N₂.
At standard temperature and pressure, one mole of an ideal gas occupies a volume of about 22.4 L. Then 42 g, or 1.4993 mol, of N₂ takes up
(1.4993 mol) × (22.4 L/mol) ≈ 33.6 L
Answer:
Option (3)
Explanation:
According to researches done by the astronomers, it has been found that the earth collided with a giant Mars-size early proto-planet, whose name was 'Theia' during the Hadean era, about.5 billion years back. This collision resulted in the detachment of a considerably huge amount of material away from the earth. The remnant debris particles accumulated and gave rise to the formation of moon. The earth during that time was comprised of molten lava only, and from this collision, the earth attained its tilt of approximately 23.5°.
Thus, the correct answer is option (3).
