Answer:
<em>Correct choice: b 4H</em>
Explanation:
<u>Conservation of the mechanical energy</u>
The mechanical energy is the sum of the gravitational potential energy GPE (U) and the kinetic energy KE (K):
E = U + K
The GPE is calculated as:
U = mgh
And the kinetic energy is:
Where:
m = mass of the object
g = gravitational acceleration
h = height of the object
v = speed at which the object moves
When the snowball is dropped from a height H, it has zero speed and therefore zero kinetic energy, thus the mechanical energy is:
When the snowball reaches the ground, the height is zero and the GPE is also zero, thus the mechanical energy is:
Since the energy is conserved, U1=U2
![\displaystyle mgH=\frac{1}{2}mv^2 \qquad\qquad [1]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20mgH%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20%20%20%20%5Cqquad%5Cqquad%20%5B1%5D)
For the speed to be double, we need to drop the snowball from a height H', and:
Operating:
![\displaystyle mgH'=4\frac{1}{2}m(v)^2 \qquad\qquad [2]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20mgH%27%3D4%5Cfrac%7B1%7D%7B2%7Dm%28v%29%5E2%20%5Cqquad%5Cqquad%20%5B2%5D)
Dividing [2] by [1]
Simplifying:
Thus:
H' = 4H
Correct choice: b 4H
Answer: 9 days
Explanation:
Let the rate of Leaf growth <em>r</em> be defined as, 
= 
where <em>A</em> is initial area of the leaf, <em>A1</em> is the final area of the leaf and<em> t</em> is the time taken for the increase in Area.
- Express the proportional relationship in equation.
Given that rate of leaf growth, r is proportional to the surface area of the leaf A. we have r ∝ A.
r = kA, where k is the rate constant.
therefore, k = 
when A = 2
, A1 = 3
so k = 
= 
÷ 2
= 0.33 ÷ 2
k = 0.167
- After calculating the rate constant k, we then find the time t when A1 is 5
- we have r = k × A1 =
so, 0.167 × 2 = 
0.33 = 
.
t = 3/0.33
Therefore, t = 9 days.
Answer:
C
Explanation:
Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces
I hope this helps a little bit
