Answer:
Correct choice: b 4H
Explanation:
Conservation of the mechanical energy
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:
[tex]\displaystyle K=\frac{1}{2}mv^2[/tex]
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:
[tex]U_1 = mgH[/tex]
When the snowball reaches the ground, the height is zero and the GPE is also zero, thus the mechanical energy is:
[tex]\displaystyle U_2=\frac{1}{2}mv^2[/tex]
Since the energy is conserved, U1=U2
[tex]\displaystyle mgH=\frac{1}{2}mv^2 \qquad\qquad [1][/tex]
For the speed to be double, we need to drop the snowball from a height H', and:
[tex]\displaystyle mgH'=\frac{1}{2}m(2v)^2[/tex]
Operating:
[tex]\displaystyle mgH'=4\frac{1}{2}m(v)^2 \qquad\qquad [2][/tex]
Dividing [2] by [1]
[tex]\displaystyle \frac{mgH'}{mgH}=\frac{4\frac{1}{2}m(v)^2}{\frac{1}{2}m(v)^2}[/tex]
Simplifying:
[tex]\displaystyle \frac{H'}{H}=4[/tex]
Thus:
H' = 4H
Correct choice: b 4H
