Answer:
Ted is correct
Explanation:
The equation for gravitational potential energy is PE = m·g·h
The equation for gravitational kinetic energy is KE = 1/2·m·v²
Where:
m = Mass of the object (The racing car)
g = Acceleration due to gravity
h = The height to which the object is raised
v = Velocity of motion of the object
From the principle of conservation of energy, energy can neither be created nor destroyed but changes from one form to another, we have;
Potential energy gained from location at height h = Kinetic energy gained as the object moves down the level ground
m·g·h = 1/2·m·v² canceling like terms gives
g·h = 1/2·v²
v = (√2·g·h)
If the speed is doubled, we have
2·v = 2× (√2·g·h) = (√2·g·4·h)
Therefore, if 2·v = v₂ then v₂ = (√2·g·4·h)
Since g, the acceleration due to gravity, is constant, it means that the initial height must be multiplied or increased 4 times to get the new height, that is we have;
v₂ = (√2·g·4·h) = (√2·g·h₂)
Where:
4·h = h₂
Which gives;
v₂² = 2·g·h₂
1/2·v₂² = g·h₂
1/2·m·v₂² = m·g·h₂ Just like in the first relation
Therefore, Ted is correct s they need to go up four times the initial height to double the speed.
