Answer:
3.64×10⁸ m
3.34×10⁻³ m/s²
Explanation:
Let's define some variables:
M₁ = mass of the Earth
r₁ = r = distance from the Earth's center
M₂ = mass of the moon
r₂ = d − r = distance from the moon's center
d = distance between the Earth and the moon
When the gravitational fields become equal:
GM₁m / r₁² = GM₂m / r₂²
M₁ / r₁² = M₂ / r₂²
M₁ / r² = M₂ / (d − r)²
M₁ / r² = M₂ / (d² − 2dr + r²)
M₁ (d² − 2dr + r²) = M₂ r²
M₁d² − 2dM₁ r + M₁ r² = M₂ r²
M₁d² − 2dM₁ r + (M₁ − M₂) r² = 0
d² − 2d r + (1 − M₂/M₁) r² = 0
Solving with quadratic formula:
r = [ 2d ± √(4d² − 4 (1 − M₂/M₁) d²) ] / 2 (1 − M₂/M₁)
r = [ 2d ± 2d√(1 − (1 − M₂/M₁)) ] / 2 (1 − M₂/M₁)
r = [ 2d ± 2d√(1 − 1 + M₂/M₁) ] / 2 (1 − M₂/M₁)
r = [ 2d ± 2d√(M₂/M₁) ] / 2 (1 − M₂/M₁)
When we plug in the values, we get:
r = 3.64×10⁸ m
If the moon wasn't there, the acceleration due to Earth's gravity would be:
g = GM / r²
g = (6.672×10⁻¹¹ N m²/kg²) (5.98×10²⁴ kg) / (3.64×10⁸ m)²
g = 3.34×10⁻³ m/s²
<h2>
Answer:</h2>
<em><u>Velocity of throwing arrow = 43.13 m/s.</u></em>
<h2>
Explanation:</h2>
In the question,
Let us say the height from which the arrow was shot = h
Distance traveled by the arrow in horizontal = 61 m
Angle made by the arrow with the ground = 2°
So,
From the <u>equations of the motion</u>,
Now,
Also,
Finally, the angle made is 2 degrees with the horizontal.
So,
Final horizontal velocity = v.cos20°
Final vertical velocity = v.sin20°
Now,
u = v.cos20° (No acceleration in horizontal)
Also,
So,
We can say that,
<em><u>Therefore, the velocity with which the arrow was shot by the archer is 43.13 m/s.</u></em>
Question: A loader sack of total mass
is l000 grams falls down from
the floor of a lorry 200 cm high
Calculate the workdone by the
gravity of the load.
Answer:
19.6 Joules
Explanation:
Applying
W = mgh........................ Equation 1
Where W = Workdone by gravity on the load, m = mass of the loader sack, h = height, g = acceleration due to gravity
From the question,
Given: m = 1000 grams = (1000/1000) kilogram = 1 kg, h = 200 cm = 2 m
Constant: g = 9.8 m/s²
Substitute these values into equation 1
W = (1×2×9.8)
W = 19.6 Joules
Hence the work done by gravity on the load is 19.6 Joules
Answer: The property that will best provide evidence that the samples are solid includes:
--> if the substance has a definite shape,
-->if the substance has a definite volume
--> if it's tightly packed.
Explanation:
According to the kinetic theory of matter, every substance consist of very large number of very small particles called molecules. These molecules, which are made up of atoms that are the smallest particles of a substance that can exist in a free state.
Matter can exist in the following states:
--> Solid state
--> liquid state or
--> Gaseous state.
The general property of a substance that is in gaseous state includes:
--> Definite shape: A substance can be grouped as a solid if it's shape is fixed that is, it doesn't depend on the shape of other materials.
--> Definite volume: A substance can be grouped as a solid if it occupies its own shape. This is due to the force of cohesion among its molecules.
--> Tightly packed: A substance can be grouped as solid if the molecular movements of the particles are negligible.
From the samples under observation by Juan and kym, if the sample that possesses the above described qualities, it is a solid rather than liquid or gas.
Answer:
Evaporative Water Loss = 2 kg
Explanation:
According to the given condition, the water entering the body must be equal to the water leaving the body. Therefore,
Water Entering the Body = Water Leaving the Body
Feed Water + Drinking Water + Metabolic Water = Urine Water + Evaporative Water Loss
using the given values:
1 kg + 5 kg + 0.5 kg = 4.5 kg + Evaporative Water Loss
Evaporative Water Loss = 1 kg + 5 kg + 0.5 kg - 4.5 kg
<u>Evaporative Water Loss = 2 kg</u>
