Answer:
The answer of first question:
The speed should be √2 times the initial speed.
v°=√2×vi
v° stands for new speed
vi stands for initial speed
The answer of second question:
The height should be four times the previous height.
h°=4×h
h° stands for new height
h stands for previous height
Explanation:
According to conservation of energy:
The energy can't be created or destroyed but it can transform from one form to another form of energy.
When a pebble throw upward it's kinetic energy converted into potential energy. So, according to law of conservation of energy
Kinetic energy = Potential energy
( 1/2 )m×v² = m×g×h
m stands for mass of pebble
v stands for velocity
g stands for gravitational constant
h stands for height
(1/2) m×v² = m×g×h
Multiply by 2 and divide by m on both sides
v² = 2×g×h
Take square root on both sides
v =√(2×g×h) ...................Equation (A).
If we want twice the height (h°=2×h), then the new velocity will be v°
Again using law of conservation of energy
Kinetic energy = Potential energy
(1/2) m×v°² = m×g×h°
v° stands for new velocity
h° stands for new height
put h°=2×h in above equation
(1/2) m×v°² = m×g×2×h
Multiply by 2 and divide by m on both sides
v°² = 2×g×2×h
Take square root on both sides
v° = √(2×g×2×h)
v° = √2×√(2×g×h)
from equation (A) we know that v=√(2×g×h)
So the equation become
v°= √2×v
The speed should be √2 times the initial speed.
Explanation for second answer
According to law of conservation of energy
Kinetic energy = Potential energy
(1/2)× m×v² = m×g×h
Divide by m on both sides
(1/2) × v² = g×h
Divide by g on both sides
v²/(2×g)= h .............Equation (B)
If we want twice the speed (v°=2×v), then the new height will be h°
According to law of conservation of energy
Kinetic energy = Potential energy
(1/2) m×v°² = m×g×h°
v° stands for new velocity
h° stands for new height
(1/2) m×v°² = m×g×h°
put v° = 2×v in above equation
(1/2) m×(2×v)²=m×g×h°
(1/2) m× 4×v²=m×g×h°
Divide by m on both sides
(1/2) 4×v²=g×h°
Divide by g on both sides
4 (v²/2×g) =h°
From equation (B) we know that v²/(2×g)
So the equation become
h° = 4×h
The height should be four times the previous height.
